Unless you pick a really crappy variety (I've seen a couple around), homegrown strawberries will always taste better than store-bought ones. Since they don't have to travel a thousand miles, there's no need to pick 'em early, and the flavor develops more fully. That said, there's still noticeable differences between varieties, and what you grow depends on a combination of which ones can handle your locality and which ones you like best.
In hotter climates, like mine, day-neutrals are most often recommended (Seascape, Eversweet, Tristar), but I'm growing a couple of June-bearers, and they're surviving just fine. Note that I said "surviving"... they're not really producing well, but I get a few berries twice a year.
The alpines, surprisingly, are the most productive ones I have. That's not saying much, but I reiterate: I have them under nasty conditions. That they're alive at all is, I think, near miraculous. As Doglips said: they're best suited to really large pots (half-barrels), and I have them pot-bound in tiny four-inch pots (I can't wait to see what they crank out when I get 'em into the raised bed!).
As to which ones are the best, that depends on your preferences. I've heard Alpines and Mara des Bois (day-neutral) being referred to as the best of 'em all (my family concurs, at least on the Alpines; haven't tried Mara yet), but I've also heard of some people saying they taste too much like candy for their taste (they probably prefer more balance with the acidity). I also have a possibly nameless june-bearer referred to as "King Kong" by the catalog my Gramma got it from, and while it's far from huge or perfect, it actually has pretty good aroma and flavor when fully ripened. This is a variety I expected to be sub-par, so it goes to show you that you'll usually get good berries at home no matter which you choose.
So if you're looking for your ideal strawberry, read up on the different varieties. Things like heat and moisture sensitivity, productivity, texture and flavor profile. Some are firm, others soft and juicy, some are sweeter, others, more acidic. Day-neutrals produce less at any given moment, but have an indefinite fruiting season, and do well where it's warm. June-bearers do well where it's cool, and have a short fruiting season with a bigger harvest. Alpines are usually ever-bearing, produce more with each passing year (at least until they get old, maybe around the 5 year mark; then you rejuvenate by dividing), and have heat-tolerant cultivars. Musks are june-bearing, and I have yet to get a single flower (not surprising, since they need more than Alpines and I have 'em under the same conditions).
There's a lot to choose from, but it's not hard if you know what you got and you know what you want.