I have a v1, and it's one of my favourites.
It's got only a handful of characters compared to recent releases, so you can get to know them well. Plus, which character you get is influenced by how you care for it, so it's still a challenge getting all the characters. I raised around 17 generations on a v5 and got all of the characters (well I'm pretty sure I got most of them anyway, I can't really remember). On my v1, I raised 104 generations and never got a Hanatchi. Ever. Or an Otokitchi, but Otokitchi are pretty easy to get (just raise a female Tamagotchi and never let it marry).
The v1 has a weight system on it, which is actually pretty easy to keep down. If you play the dance game (you only need to be 2g above base weight to play it), you can lose 2g of weight after just the first round. If you play the jump game (you need to be 3g above base weight to play), you can lose 3g of weight after just the first three hurdles, which are pretty easy anyway.
The v1 never annoyed me with mail and school and all that. The v4 always drove me nuts about raising the skill points to get a job (yes, I know it didn't take long, but I thought the games were far too long and annoying, especially Dance), only for the Tamagotchi to get married, have a baby and depart pretty soon after. I felt more attached to my v1 than to any other of my Tamagotchi (I also own a v3, a v4 and a v5). Though it might be because it was my first Tamagotchi. If only I hadn't run through some sprinklers that day a couple of years back without thinking... It still works though, just that you have to press the A button pretty firmly. If it wasn't for that, or how I tend to get kinda stressed raising it at times (because I have already raised 104 generations and if one departed I'd have to start over right from 1st generation again), the v1 would definitely be my first preference to start up again. (Yes, I know my signature says that I'm on the 99th Generation but it's a bit outdated because I haven't been on TT in a while.)
I have one, and it almost broke one time, and I almost cried D: I LOVE the characters on there. They seem so original. Anyway, the only thing I DONT like about them, is the games D: I awlays hit the Dance game, WHICH I HATE WITH A PASSION, and it drives me up the wall. The weird thing about v1's is you can exit out of the games 
