I'm similar to Hosfac in general play. Creating one sim with a vague idea of maybe completing the inventing skill and making a time machine, plonking them down on an empty plot or a starter home and trying to achieve my goal. I often get sidetracked along the way, finding a partner, having children and usually end up just making sure that my sim is happy. Consequently, I still haven't made a time machine and I've had the game almost since it was first released
. I always play with free will on high and story progression on, I seldom use cheats except in build-mode, though will use the money cheats at times. I've learnt much more about the other characters in the neighbourhoods through coming on here and browsing the threads, than I have through playing the game. I like to read about what other people are doing and how they play.
As for ideas for you, I've played The Sims 2 as well, and have tried most of the different game play ideas. Some do not translate quite so well into TS3 but at various times I've tried:
An Asylum Challenge - creating 8 sims of various personalities (making sure that each are at least neurotic or insane), building them an asylum but furnishing it with beds and seating for only 7 sims, one bathroom and one cooker. All the sims enter the asylum but you control only one of the sims. Sometimes it can be mayhem - the fun part, for me, is that I get to see interactions that I never see when I normally play.
I've also had a go at something similar with one controllable young adult sim, an elder and six toddlers. For that one, though, I made sure that there were enough beds for everyone. It was stressful at times, what with the threat of the social worker, but strangely enjoyable.
Rags to Riches (Poverty Challenge) - starting one sim off with no money at all. (If you don't want to use cheats then you buy a plot and fill it with landscaping to use up all your cash.)
The Pretacy and Uglacy Challenges are more fun if you are playing at the same time as someone else and you both choose the same starter sim. The Pretacy takes an ugly sim and you see how many generations it is to make them pretty - with the Uglacy, you start with a pretty sim and then compete to get the ugliest sim within a given number of generations. It's all subjective though - peoples ideas of beauty really vary.
Living off the land - no work for your sim at all. This is really not a challenge in TS3.
Black Widow - start with young adult female, the aim is to see how many husbands she can outlive. (I've never completed this, sadly I really don't like killing off sims.)
The Challenges here, created by Metropolis Man are an excellent way of exploring all the game play options. Since joining in I've done things that I never believed I'd be able to do. I don't score high (I get distracted and like to keep my sims too happy) but I really enjoy giving them a go. Some of the challenges, though they seem really daunting at first read, have been very enjoyable to play.
Have fun and hope you enjoy it here on this most friendly forum.