I'm a little confused as to what you mean by incubator.
Are you talking about an incubator like Tech Stars or Y Combinator in which you bring in teams and help them with the development process? If that's the case, wouldn't the decision for which engine to use generally be left to the people running the individual projects?
You may decide to focus on Unity and UDK, sure. But what about when someone comes in wanting to make a purely 2D game, and they've already developed a large code base on top of something totally unfamiliar to you like SDL or Monocle. I'd say you'd be better served diving into a project using whatever tool makes sense at the time and building your general knowledge so that you can help future teams that come through.
The only other type of organization that I can think of as an incubator would be a sort of collective, where you work on projects and provide a way for people to come in and get experience working on a game. Then your concern about choosing an engine would make a little bit more sense. Even still, you would have to factor in the skills and professional goals of your first batch of team members.
What languages and libraries are your programmers familiar with? Do you have programmers? If you have all pixel artists then forget about UDK or Unity, look at something 2D like SDL, SFML, or even Flash with Flixel, FlashPunk, or the standard Flash graphics api. Since you say your background is in web development, maybe think about a design with multiplayer, or at least something that would require or benefit from storing player statistics in an online database so they could be publicly viewable through a web interface.
A group that I worked with initially started writing 2D games in C++ with SFML. Later we switched to as3 and Flixel to reduce development time. Then we decided to give XNA a shot since a lot of our artists were primarily 3d modelers and animators and wanted to be able to hone and showcase their skills in that area. Unfortunately that project ended up going nowhere because it was chaotically managed and blew up in scope. That's another thing to consider, you probably don't want to start off the bat with the kind of project that UDK would be useful for.