Hi, quite sadly you'd be limited to 3Gb RAM with a T60. I had retired my T60 some 5 years back or more because I felt performance on it - even under Ubuntu - was not sufficient. However I'm absolutely happy now with my X220 and T520 (ssd, 16Gb RAM each, 4337 dock).
Do you feel like you must use a 4:3 screen? If so wasn't there a T61 14" in 4:3? Also there definitely was an R61 in 15" 4:3 and possibly in 14". But note: both T61 and R61 require DDR2 RAM, so if you want to get 8Gb there it will be super expensive - or you won't find it at all. You'd need 2 sticks of 4Gb - rare/expensive.
If you're okay with 16:10 screens I suggest you start looking into fresher models starting perhaps with T400. (Make sure it takes DDR3 that is dirt cheap, but I think it does). There were some T410 I believe.. Though I don't know these generations well..
If you're really okay with 16:10 If you're okay with 16:9 I can assure you that *20 family: X220/X220t/T420/T520/W520 feel quite modern performance wise and once you upgrade them to SSD and >=8Gb RAM you will definitely be able to use them for whatever you like same as myself

If you want a bit more battery life go for X230/X230t/T430/W530. The bodies of all *20 and *30 families are classic enough in my view: they are nice, sturdy machines (even if edges of screen bezel and palmrest chip off easily on X220/X230). Because they are slightly younger than T60 they also can look better. They are slightly less heavy than T60 but still as strong/classic. And it's easier to find batteries for them - even if aftermarket.
If you feel like getting a classic keyboard - everything up to and including *20 family have them and they can be fitted into *30.
P.S. why don't you fill out country in your profile? Think forum rules gently nudge you into doing that