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for cart based games any atari will do, XEGS, XL or XE.

for 90% of disk/cassette games again any will do.

Some games will uses the extra 64K in the 130xe for "enhancements" to the game. I think games like mercenary used a higher resolution graphics mode.

The main difference between the three machines is the expansion port on the back of the computer.
XEGS has not got one.
XL has one and separate cartridge port on the top of the unit
XE has the cartridge port on the back of the unit and a second port next to it that contains extra signals to allow external devices
most add ons for this expansion port come in two variaties, on for XL and one for XE.
however there were only a few add ons for this expansion port.

I would say, if you go for an XEGS make sure you get a keyboard for it, as this will be needed for a lot of games

Also if you want to play games with the light gun, you will need a old style CRT TV or monitor. It will not work with newer flat screens.

My Lynx screen went bad about two years ago, I replaced the screen and every thing was fine.

That was in Europe. I was wondering if there was bad batch of screens. If there was, it is a wide geographical distribution.

or maybe they will all start to go bad, and some have gone a lot sooner than others? That would be worst case

My first thought was the 130XE, and if I could have only one that is the one I would choose.

But my favorite would be the 800.

I could only afford a 400 when I was young, but I always wanted a 800. There is something, about the design of the 800 that always takes me back to my childhood.

Wow. Postage to Europe is $161.99 UPS Worldwide Saver

But, there are compilers for BASIC:

I found the manual for one here:
http://www.bollwerk-...ic_Compiler.pdf

Compilers should shrink the size of the program and make it run faster. It will however no longer be listable or editable.

If this is really what you need I would suggest looking at Turbo Basic. This mainly backward with atari basic and has a compiler.