I grew a bunch of subtropicals (not ultratropicals, mind you) when I lived in apartments in NY. It was fairly easy. I did not grow much in the way of fruit trees, other than my lemon tree, but a number of different kinds of flowering plants, and vegetables, etc. If you want to put effort into it, and don't mind some loss through trial and error, it's very doable, and the experimenting is fun. Obviously, as the size of the collection increases and the need for output gets more strict, so proportionally will your fun decrease. But, assuming you're just doing this as a hobby and not to live off the food production or for commercial gain, you'll be fine. I've written quite a few posts in the past on some of my tricks to be successful.
I never had money for a greenhouse. I found simply changing out indoor light bulbs with full spectrum bulbs, and keeping the air around the plants somewhat humid, was just fine. You need to be patient with Northern tropical plants, don't expect a lot of growth, or for it to be easy to make them flower outside of summertime... but you can certainly keep them alive and watch them grow slowly, and for not that much money. Invest in good organic soil - they're going to be suffering in so many other ways, this will tend to help them through the rough times. The greatest thing I ever found with container gardening is to recycle old non-biodegradable styrofoam peanuts. Simply buy a pack of cheap plastic grow bags with holes, which yes will eventually degrade but especially if not outdoors will last a few years just fine. They cost pennies, and can be shoved against each other and against walls to form basically any shape you need. They can also be easily stacked on top of each other if you have plants of different sizes, so you can water them all at the same time and save space. Fill with the styrofoam pieces about 2/3 of the way full. Top off with 1/3 full of soil. So there's not actually much soil, but it's enough for nutrition, and the plants' roots LOVE the peanuts... they shove right through the styrofoam. Sooo easy and cheap to put together, excellent oxygen and drainage, and extremely light to carry around from one room to the next, or outdoors in the summer. Sit the bags in a pan or tray of some sort to catch the water, so they can stay humid, and sometimes self-water with the extra when the roots get long enough. Put aluminum foil around the inside of the top, and facing in toward the plants - it will help light reflect from windows and from lamps to give the plant more than it would ordinarily get from just one side of one limited window, keeping the exposure around the plant a bit more even.
There is some disagreement about optimal light hours for tropical plants, but it will depend on which species and how old it is. Think about their natural conditions when they grow wild, if they are likely to be beneath a canopy of tall mature trees, or growing out alone in the sun in a field. Generally speaking, most people seem to say optimal growth can occur if you provide between 12-16 hours of light a day. Not more - the plant needs time to rest. You can do far fewer hours of light, but don't expect the plant to grow much. Another option is to use a box light like people use for Seasonal Affective Disorder. You can sit with one surrounded by your plants, and when you're done leave it on for the plants to enjoy. Most are not expensive to keep running for many hours. Sometimes you can buy used ones fairly cheap. On the subject of used, you can also call around for places getting rid of styrofoam peanuts, or put up a craigslist ad, if you don't happen to have a bunch. Recycling is best - no need to buy them new! Make sure they aren't biodegradable (usually greenish), or they'll melt in water.
At a certain low temp they will drop leaves and go dormant. Do not water almost at all when in this state - mold and root rot are your biggest risks for indoor plants like this. You can scratch the surface lightly to be sure it's not dead - if there's still green, you're fine. Don't disturb the roots much - be careful any time you move the bag. Indoor plants will tend to be very susceptible to aphids and spider mites, and sometimes scale. Keep a bottle of pure neem oil mixed with water on hand, and spray regularly. It doesn't make the house smell great, but Neem has a lot of amazing medicinal qualities so won't hurt you.
Consider also dusting the plants with Diatomceous Earth.
If you then take them outside, never do so until the weather is consistently always 60F or above, even at night. Don't rush it.
Harden them off slowly, being cautious to only give them a few hours of direct sunlight at a time. PATIENCE is key when dealing with indoor tropical plants! It should take you a week to 2 weeks to get them to their final destination, depending on whether or not they will eventually end up in full sun. Again, the styrofoam bag works wonders at this time. But, make sure it is tied around the top or leaned against something sturdy, so strong winds won't blow all the soil off and the peanuts everywhere, or knock the plant over. If possible, do the same process in early Fall before bringing them back in again, so they get used to less direct sunlight. Never leave them out if the temps with go below 60F... they will get sad. Of course, that depends on which species, but as a general rule if you're trying to grow tropics it's better to be safe than sorry with your investment. I used to think light was the most important thing - it's not. It's warmth, and humidity, and good drainage. Light is like 4th on the list. Plants in the tropics have to deal with deep shade all the time, and they simply grow around it to try to find a light source. They can withstand low light for months (but don't stick them in a closet). What will kill them faster is being too wet or too dry, and then too cold or too hot.
Don't burn them by placing against the radiator. Don't freeze them by putting too close to the window. If warmth is a problem, you can save a lot of money by using string holiday lights. The temp of the air doesn't actually matter, it's the temp of the PLANT. String lights are cheap to buy and to run, can be arranged to look pretty, and usually keep the plant relatively warm in sub-par temps. Spray the plants' leaves and top soil regularly with a water bottle when you walk by. Do this enough to keep dust from accumulating on the leaves, which will suffocate the plant. Keep them close together so they can develop a microclimate of humidity in the house. Consider tenting them with clear plastic to keep the humidity in - heating systems are extremely drying (as are air conditioners). There are even mini greenhouses for sale that are essentially a green shelving unit with a clear plastic sheet over it - you can stack the plants vertically, turn a single strong lamp toward the whole thing, and find a way to regulate humidity and temp just right for all the plants inside, without making your house look like a total mess, or taking all your floor space. But if one plant develops pests, expect them to spread like wildfire in such an environment - spray with Neem weekly!
The whole setup can easily cost under $100, including a few seeds to get you started. My highest cost was actually the soil, which I had to ship to my apartment. But I found one 2 cu.ft. bag could cover about 3 10 gal plastic bags of styrofoam peanuts, and more if I really wanted it to stretch to start off a small plant. I could always add soil later - which I usually do in the form of shoving my composting down into the bags throughout the year... fruit peels and vegetable scraps and paper towels, kleenex, etc. It seemed to work just fine, and kept my use of the city garbage really low.
I moved many times, and found plants in this type of setup are fairly easy to move. Usually I have to slip on a new bag under the old one first, because by then likely the plastic has kind of weakened and I don't want a spill. But, overall, it's pretty cheap and easy. Sturdy plants will survive, if not thrive, for multiple years this way, and as long as they get enough light, warmth, and water, can even flower and fruit. Then you just need to learn hand-pollination, which is easy with a manageable number of plants.
Good luck!
There are many great plants to grow for container gardening... do a search here to see lists of plants that fruit at small sizes. But I also urge you to grow tropical vegetables (and visit our sister forum for ideas!) and edible flowers, which take up little space while being highly useful, easy to grow, and often very attractive. Plus, usually they come with a ton of seeds so if they die before reseeding themselves, it's no huge loss, just start again!
P.S. I've made this point before, but if you're looking for more tips, there are a ton of marijuana forums that are actually extremely helpful, and often rather professionally written. People on this forum tend to naysay growing tropicals indoors, but a huge market grew (literally) out of growing semi-tropical plants in people's closets and basements in cold climates. I'm not one for illegal drugs, but those people had a high stake in having a successful and often organic product, and they are some incredibly informed farmers. They are some of the best plant experts in the world when it comes to growing organic warm-weather plants indoors, which are the most challenging conditions to grow in. Anyone can grow tropical plants outdoors in a warm sunny climate with chemicals. What's really hard is to grow such plants in the opposite environment of pretty much everything they want, and not have any artificial chemicals to lean on, and still be successful. I've learned a lot from searching the internet and accidentally falling into those forums repeatedly.