I’ve got a hand-me-down accordion from my father. He grew up in the Camden area of north Minneapolis and a door-to-door accordion salesman convinced my grandparents to buy him the accordion which is now in my possession. Gone are those days of immediate accordion consumption and we’re left with Lawrence Welk reruns on PBS.
As for my accordion, I can’t find a name on it (I’m sure if I opened 'er up, I would). It’s a lumbering beast and still plays quite well (23 lbs is considered ‘light’ in the full-size accordion world). The billows are worn but still completely functional. Your left hand plays the bass notes and your right hand plays the melody. Your left arm will bulk up as well since this is the one which will be doing most of the work pushing and pulling.
I’m not sure where you’re located, but an antique shop might be a better bet to finding one. Make sure to ask before playing as some folks don’t care for the sound or it could fall into dusty pieces. Make sure that all of the buttons and keys produce a note. I’d be hesitant to buy a used one off of eBay. As with any instrument, unless you know the specific brand and model and are just going for a better price, you could end up with an instrument you don’t want. Each accordion has a different timbre. Some are mellow and low, some are reedy, and some are ear-piercingly bright and sharp. (It seems to me, the more expensive, the more mellow it is.)
There are different sizes of accordions. Some with bass keys that go on for days (and are what seems to be completely random order at first, but I believe, IIRC, are arranged by 5ths.) This is a daunting part of the instrument as they are not labeled ('cept the C which has an indent on it on mine). The more keys, the more to learn. Here’s a dizzying map.
Of course, with any instrument, perceived value and sound goes up with price. The more you spend, the better the instrument. Not always completely the case, but it’s a good rule of thumb.
If you want to do an introductory instrument to accordion, try a concertina. They’re smaller, relatively cheaper, and simpler to learn. There are several types with varying complexities (anglo/english/duet with some having the same push-pull note and others having it be different note like a harmonica).
I’m not sure where you are in the world, but locally for me, there’s a store called Hobgoblin Music down in Red Wing, MN or Lark in the Morning (which sends wonderful catalogs full of musical instruments to taunt me in my dreams).
I’m sure I’m forgetting lots of things here.