Somebody already wrote on another thread that they grew meyer lemon seeds and they all come out different. Some were like Limes some were like tart oranges. It's not a real lemon, instead a hybrid with different stuff mixed into (though mostly lemon) so you can get many different results from the seeds. I think it will be fun to grow from seed.
Usually you get fruit around 5 or 8 years old from seed. So it should be getting fruit soon. I don't think the climate will make any difference. But if you grow from seed it is usually a bigger tree compared to rooting a branch. A rooted branch meyer lemon is very small. The regular variety I think maybe 8 or 9 feet maximum size (closer to

and there is a smaller dwarf variety that is about six feet maximum size. It always has big thorns though.
It shouldn't get much bigger- meyer lemon is one of the smallest citrus. Maybe 12 feet at the most from seed I would guess. Though it can grow very wide.