I've played all of them except 4 so I'll give my pros and cons for all of them. Hopefully this will help you decide!
TS1
Pros:
-Nostalgic
-Simple - there aren't as many things you need to do or think about as other games
-No ageing gives you a lot of time with your sims so no need to rush anything
-Can probably be found for very cheap, as it is a very old game.
Cons:
-Harder to build houses than later games
-Gets boring quicker than other games because sims don't age
-Not as much to do as later games, even with expansions
TS2
Pros:
-A lot of content and things to do, especially if you get the expansions
-Runs quickly and smoothly, a lot better than 3 imo
-Looks nice graphics wise, not a huge difference from sims 3
-Adds a lot more features that are not in Sims 1, such as aging and more life stages, which make them game more interesting and realistic
-Certain things are not as frustrating as 1, eg getting sims married and to the top of jobs is a lot easier
-There are a lot of amazing mods and custom content you can find online and if you are reasonably careful they won't ruin your game at all
-Again and old game, so you can probably find it cheap
Cons:
-Lacks some of the realism that Sims 3 has with the open world and all sims in one neighbourhood ageing at the same time
-Sims do not have as much personality as they do in 3
-Less customisation options than 3
TS3
Pros:
-Each neighbourhood is like an open world. You can freely explore and go to different lots without having to sit through any loading screens.
-All sims will age as you play, regardless of active family, so you don't have to play all families equally in order for them to age at the same rate
-Create a sim is dramatically improved. There are a lot of customisation options and sims have more interesting and diverse personalities than in 2
-You have more options when building and decorating houses
-Similarly to 2, there is a lot to do if you have a few expansions
Cons:
-Can be VERY glitchy. This is a big con, as this has ruined the game for a lot of people.
-From what I remember, the base game alone doesn't have as much to do as Sims 2's base game
-There are more expansions and they each offer less and are more expensive than Sims 2 games so it will cost you more
-Custom content and mods are trickier and more risky to install than in Sims 2
So that's my run down. If you have any more questions, feel free to ask me, as I have played A LOT of Sims over the years. Overall, I'd say my favourite is Sims 2. From my experience, it runs a lot smoother than Sims 3. There is also just as much to do it my opinion and you only miss out on a bit of realism and customisation, which I can easily do without. Sims 3 is great too but I wouldn't bother unless you have a good computer and even then you'll probably have a few problems with glitches. I personally play both 2 and 3.
- - - Post Merge - - -
TS2. Nothing else like it.
TS3 is nice for the customization and open world but it has a lot of issues, and it doesn't have quite the same charm.
This is pretty much a perfect short summary of what I think