Assume for a moment that you were a PC game producer with limitless funds. What game would you have developed and what studio would have develop it?

The obvious answer is Half-Life 3, developed by Valve

my own studio - and a game perhaps with similarities to, but still ulnlike another you have played. DRM free of course!

A modern day setting realistic style rpg could be somewhat unique. It could be based mostly on dialogue options. Think of a how a drama tv series works. Basically it could be like Heavy Rain but with the kind of dialogue options of Mass Effect and would be a "choose your own story" style game.

Quantic Dream could do it.

Am open world game like the Elder Scrolls games, with Radiant AI that actually works as it should, with the dungeon crawling of Ultima Underworld, stealth gameplay of Thief and combat of Dark Messiah of Might&Magic.
No quest compasses.
No DRM.
Developed by Looking Glass Studios/Arkane Studios.

I would fund a game by A Sharp in a similar mold of KODP but about a wandering mercenary army (in the vein of the "Black Company" novels) instead of a village from the Heroquest universe. The base of the game would be managing a mercenary army as it travels a fictional world, taking jobs, and subtly changing the course of events in the world (based on the players actions). Think of it as Star Control 2 meets KOPD meets Sid Meier's Pirates.

Sounds like something a big publisher would do.

A horror-action FPS like Blood. I'd say Monolith or iD could do it well.

Or a Victorian-Era horror RPG developed by Obsidian.

Sim-Morgue

I'm really serious about this one. (If one of you takes this idea, makes a billion dollars, and doesn't even bother to mention me in the credits I'm gonna be pissed!)

Anyway, all the daily struggles of 1st building and organizing the morgue then the struggle of running a morgue with bodies coming in and out and keeping everything neat and clean and organized. Then you add scenarios like a body that comes in as "natural causes" is obviously "foul play" and it's up to you to rectify it. Another great one could be a "living dead" scenario to shake things up. The possibilities are limitless.

As far as company, I don't know enough about those. Anyone but EA or Lucas Arts I guess. One things for sure, put it on sale here. I don't think any other game site would quite appreciate the genius of it.

there is really only one answer:

PSYCHONAUTS 2 - come on Double Fine, I know you want to.

I have a few:

1) A Xenoblade Chronicles like game but with Radiant AI, an ever changing world based on the decisions you make, and super huge monsters to fight. Developed by Obsidian, Monolith Soft (I'd buy them if Nintendo wanted to get rid of them), or any other developer familiar with this sort of thing.

2) Half Life 3 by Valve, which would be released on GOG DRM-Free of course ;)

3) Terraria Remade with new content and actual (or at least good) mod support, and release it here and on the developer website DRM-Free

Sequels to Grim Fandango, Full Throttle, Monkey Island, Psychonauts,Sacrifice, Legacy of Kain,Commandos (topview not that sh*t shooter) and Silver!

In a nutshell, I would make an open-world Mass Effect game. Bioware and Rockstar North would collaborate.

A looter shooter much like borderlands but with a more serious cyberpunk tone and a heavier emphasis on story and choice. I'd cherry pick the dev team from a bunch of the greats.

That or I'd scam gamers by making something very half arsed in an underutilized but much wanted genre and embezzle as much of these unlimited funds as I could before running off to retire on a tropical island, I'd also rename myself Sergey Titov in honour of the man who gave me the idea.