I've gone through this thought process a few times, but I admit that I've not been very consistent in following through whenever I did make a decision. Often, just when I have decided to not buy any newly released games and wait until they hit the discount bin, an exciting title comes out that I just have to play. Even when I plan on buying only major titles in the genre, some never heard of game pops up that sounds so good that I simply must have it.
But sometimes I do succeed, and that's when I try out open source software and look for discount offers in my local store or at GamersGate. I'm no longer so much in love with the latest graphics, so that helps (I still bought a new video card for 250 Euro last year). There are plenty of gems to be had, and when a game has been out for a while, it usually has been patched and there are plenty of reviews. The downside is that the communities aren't always active anymore, which makes the whole experience a little less exciting. Being part of a new, evolving community is fun.
I've also had a phase where I bought mostly handheld games for the DS and the PSP, in an attempt to get more bug-free games and to get away from having to upgrade my computer every so often just to be able to play games without stuttering or other performance issues. This worked quite well for a while, but I started to miss more complex strategy games that aren't so common on handhelds, although they have a neat selection of turn-based strategy titles.
I've also gotten into Go, the Asian board game, figuring that it's a timeless strategy game, and that all I learn about it is "forever". I still play Go, and I believe it truly is the most fascinating strategy game, but it's abstract and like you I grew up with video games (got my first computer in the early 80s, and had an Atari 2600 before that), so the "need" for video gaming surfaces frequently. Go also didn't save me any money! I gathered a nice collection of books and imported semi-precious Go stones form China. Oh yeah, and a 12kg heavy Go board also. I could have bought quite a few games just for that! (Thankfully I resisted the temptation to buy Japanese shell and slate stones.)
I guess none of this is very helpful! The best approach is probably to just pick up older games when they are discounted. A year or two, and there are also games that age really well and that can be played for years. Dominions 3 is a good example, but also Age of Wonders 2 or the Civ series. Anything that's designed in an open way, allows modifications and supports randomization. 