Amiga, Commodore 64, and Dreamcast in no particular order, for the combination of great libraries to choose from and difficulty in getting hold of the games. (The 64 versions of the Ultimas would make me swoon.)

1) Sega Dreamcast
2) Nintendo 64
3) Super Nintendo
I was / still am a HUGE Dreamcast fan, so it's easily #1. I would love to see N64 games here because some of them are unplayable these days due to terrible framerates. It was a toss-up between the SNES and Genesis for #3, but I went with the SNES since I didn't have one as a kid (whereas I had a Genesis), so I missed out on a lot of good games.
The huge variable for me is whether or not 1st party titles would be included. If they are NOT included, then I would have to reconsider my list and give more thought to including Arcade.
I know this is against the rules of the question, but I have to support the Sega Saturn and if it were an available option, it would be either #1 or #2. And if it could include Japanese games, it would be #1 easily. I'm left with a glimmer of hope since the two major Sega systems surrounding the Saturn were included as options. Unfortunately, from what I've gathered, Saturn emulation (and coding in general) is not a pleasant experience.

Nintendo 64
Dreamcast
Genesis
Nintendo 64 has some real beasts of games I'd love to relive, but am not going to ebay them for hundreds of dollars (I'm looking at you conker...)
Dreamcast was not the most successful system so will likely lead to alot of gamers finally getting to play games they missed
Genesis.. this is a bit of a selfish one, I had a Mega Drive, and simply would love to play all those games again

I vote for arcade games. Consumer level consoles and carts are easy to find in thrift stores and such. Buying arcade boards is a hassle I would be glad to give up if afforded a legal alternative. And I can only hope GOG will have more success than StarROMs.
Less enthusiastically, choices #2 & 3 would be N64 and SNES, respectively.

I'd have to vote for Amiga, Dreamcast, and arcade (although my unlisted dream choice would be Saturn).

1. SNES
2. N64
3. Sega Genesis

SNES, Dreamcast, Nintendo 64 - no specific order, but I would preffer only the real classics, especially for SNES. Not just some games only because they are old.

1. Amiga
2. Dreamcast
3. N64

1. Sega Dreamcast
2. NeoGeo
3. Arcade
DC support would be amazing. Nintendo 64 is also a great choice though.

1) Amiga
2) Arcade
Most of the interesting stuff from consoles is easy to get (in a legal way I mean), getting the console and buying cartridges for the most celebrated game is something you can do without big problems, or you could use VC service and buy compilations packs.
But getting a second hand Amiga and buying games is a bit hard, I have no space to place an Amiga and getting many games is a bit hard. It has a big library with some great gems from one of the best periods of videogame story, would be a great addition.
Pretty much the same for arcade, would love to have a legal way to purchase and play some arcade classics and having GoG preparing a "click to play" install.

-Super Nintendo
-Sega Genesis
-Sega Dreamcast
I'm leading with the SNES because it had had a fantastic library of titles, and the art styles in most of them have aged well. There were so many good JRPGs (Final Fantasy, Front Mission, Chrono Trigger, Secret of Mana, Star Ocean etc etc etc!) not to mention Super Mario World. Bring It, and I will Buy It.
Genesis comes second, for similar reasons. While IMHO the library wasn't as strong or as timeless as the SNES, there are still a great number of gems that I think will hold up, and that I would love to play again. These include the Tactical RPGs Shining Force I&2 and Langrassir/Warsong, the more western RPGs D&D: Warriors of the Eternal Sun (Was like a D&D themed Ultima title) and Shining in the Darkness, and obvious classics like Sonic.
Dreamcast rounds out my list because there were a number of great titles there that most people never got a chance to play. It's on the bottom of my list, though, because (again IMHO) older 3d games just don't age as well as older 2D sprite & tile games. I can still play Super Mario World and get sucked right in, but I find it hard to get back into those first generation 3D games (Crazy Taxi, Mario 64). The low polygons, low-res textures, and dangerous lack of AA just throw me off!
There were some great titles that were only released in Japan, but have since become more popular here as a result of emulators and fan-made translations (I'm looking at you Seiken Densetsu). How feasible would it be to see those games with their translations on GOG?

Without trying to imply that arcade or console games wouldn't sell or interest me, I think for a distribution platform such as GOG, computer games are ultimately more suited. Arcade games, and to a lesser degree console-style games, are more for the quick superficial fun, and I think more deep and complex computer-style games are a better fit. That's why I would choose the Amiga because of the large number of titles with exceptional quality that platform brought forward. Other computer platforms are too old for a real return value I think, except if you were going for sort of "20 C64 games for $5.99" offers. I just don't think that C64 games are big enough to function as single-game purchases these days.

1) Dreamcast
2) Amiga
3) Arcade
The Dreamcast is an amazing console that did not get the chance it deserved, and there are many great games for it. It also is not covered by any currently available distribution methods (WiiWare, XBLA, PSN) as far as I know, so it would be a great candidate.
Same thing happens with the Amiga. I never got around to try it, but it is also a well loved machine among old-schoolers, and emulation is not straightforward, at least not for the later, more demanding games.
Arcade. Depending on the title, they are also not already available to purchase on existing digital delivery methods.
I would rather have SNES and Genesis as 2nd and 3rd choices, but I see them as much less likely to happen.

1. Dreamcast
2. Super Nintendo
3. Nintendo 64
Amiga games would also be amazing, as would the other consoles. SEGA keeps releasing old Genesis games, so I'm a bit tired of seeing them.

1) Super Nintendo
2) Sega Genisis
3) Nintendo 64