Will I able to play gog version of Fallout 1 and 2 on Win7 if I buy? I've tried my original cd's after so many years and couldn't make them work :(

Fallout 2 for sure will work, there are fan-made patches that make it possible to run on Win7 (just make sure not to install games to Program Files directory)
Not sure about F1 though.

Both gog Fallouts work on Windows 7 without any patches. Although F2 presents some visual glitches on 64-bit systems. This can be easily fixed by copying ddraw.dll from F1 directory to F2.

Given that I've just bought Fallout 2 and that I'm running one of those 64-bit things, how would I get that .dll? I own the "old" Fallout collector's pack, and none of those games work on my system anymore, but would the .dll still be good?

Give me your a-mail addres and i'll send it to you.

I really appreciate the help, but I was dastardly enough to actually get off my ass and do some research, here's what I did and what's now working for me:
1) Install Fallout 2
2) Install Killaps patch (Purely for bugfixes)
Link: http://www.nma-fallout.com/forum/dload.php?action=file&file_id=704
3) Install Fallout 2 High Resolution Patch v2.02
Link: http://www.nma-fallout.com/forum/viewtopic.php?t=42386
4) Open f2_res.ini and paste over the entire [Main] section with:
[MAIN]
;################################################################################################### ###############
;Set the screen resolution here
SCR_WIDTH=640
SCR_HEIGHT=480
;Set the number of colours here
; 8 for 8bit(original)
; 16 for 16bit colour (set only if your not using Sfall with graphics modes 4 or 5)
COLOUR_BITS=16
;Position of the Hi-Res Settings Button in the Main-Menu: valid positions are 1-7.
HI_RES_BUTTON_POS=5
5) Play Fallout 2 (And kiss your social life for the next 2 months or so goodbye - No one will remember your name)

Thanks guys.

THANKYOU!!!!

For everyone who may still be having trouble with color problems or display problems with black screens, etc., check out this link. Randomnly found it in a topic on gamefaqs and it helped fix any display issues for me. If it doesn't work the first time then restart your computer and try again, it worked for me when the tool randomnly didn't work sometimes (probably just my computer). Hope this helps.
http://blog.macuyiko.com/2009/07/solving-color-problem-red-grass-purple.html