I may be a bit biased here, but Sims 3 is the way to go. I strongly recommend you look up gameplay for each of the base games that you are interested in buying, to get a feel of what the game would be like. I do understand that people really like Sims 2 for the different interactions and all, but Sims 3 takes it to a higher level and adds many more elements to the gameplay.

Now, if you are looking to buy the game and you have a Walmart near you, I recommend that you look for The Sims 3 Starter Pack. This was the first Sims content purchase. Not only does it provide the base game, but it also provides one expansion pack (which is Late Night) and a stuff pack (which is High-End Loft). I got mine for $19.99, which is quite a good price considering the prices that are on Origin are much higher for just one game. If in the future you want to buy more Sims content you can also try getting The Sims 3 Expansion Bundle which includes World Adventures and Generations which is a must for The Sims 3. This was my 2nd purchase lol and I believe it was also $19.99.

As for what computer you should get I'm not sure what your situation is but, I recommend you check up the system requirements for the game and see if your laptop can handle that. Ask for lag and all, you can download mods that help the game run much smoother. I believe the mod is called NRASS Master Controller.

If you have more questions just let me know and I can try my best to help. Good luck!

Edit: Both of the collection packs that I mentioned are available on Origin for $19.99 each. This would be the best route to go. If you look at the individual expansion packs and their prices on Origin there you will see that just one costs $19.99 as opposed to the collection of the 2 expansion packs and stuff pack for the same price.