The biggest factor in deciding what shows to make is money (Surprise!). Most anime studios don't have the financial resources to invest in a movie or even an OVA themselves so they need to work with a sponsor or sponsors. The sponsors invest their money in the production and own a share of the proceeds usually equivalent to the percentage of their investment in the budget. Whenever the producers try to do an entire movie without paying for it they hit difficulties. First they call the director, who is usually either on a mountaintop in Tibet contemplating the true meaning of human existence or in a strip-bar contemplating college girls' uncovered buttocks, and ask if he will do the movie. He usually says yes so they don't have to worry about him until he wants to spend some money on the project which is usually immediately in the case of the strip-bar (Directors always want to write the bill off on the production expenses).
Next the producers call the enshutsu, character designer and animation supervisor who are all smart (or at least lucid) enough to know they are trying to scam them into spending an entire year working for free so they usually hang up pretty quickly. The producers huddle in a coffee shop, smoke about 1,100 cigarettes in 2 hours and say, "That's OK. We didn't want the creative management anyway."
They next go to parks and find animators who haven't been able to find projects for a long time living in cardboard boxes and offer them ramen and saltine crackers if they will draw the whole movie.
They have videotape that could be made public of the music director trying to learn to play the bagpipes so they're pretty sure he'll do it for free. They decide to do it digitally so they don't have to go look under bridges for cel painters, so they "hire" some students. Students always work for long periods without pay. They can just keep promising them money and then lock them out of the studio some morning.
The evil plans of the producers usually last about 45 minutes. (There are no doubt producers somewhere who have bought a million monkeys and have them beating away on computers trying to recreate AKIRA...) I've had people call me up and ask me to direct some project they have and about halfway through they say that I will be paid with a percentage of the profits and that would be much more than if I was to take one of those salary things which nobody really wants anymore.
Sponsors have access to distributors (which most anime studios don't) which is extremely important because, if your work doesn't get distributed and sold, then you don't make any money from it and you can't make any more. A large part of the projects come from sponsors themselves. Somebody comes up with an original project and pitches it to a large publisher or music company or video distributor and they decide to produce it. Sometimes a publisher gets a producer interested in animating a popular manga or a novel. Many companies feel that it is safe to animate a popular manga because it is already "tested" and there will be a guaranteed audience. The same thinking is also applied to games - if the game is really popular then most of the fans will buy ancillary merchandise, including OVAs. (This, of course, is not always true and the companies know that.)
An example of this would be Kodansha approaching Bandai about co-sponsoring the anime production of a popular comic. It could just as easily be Bandai approaching Kodansha though.
Many producers feel that an extension of an existing popular show is "safe" as well. As previously mentioned there is usually a flood of ideas by people wanting to do something based on an existing show. The ones most often chosen are those of the original creator and the chief producers. If somebody can find a way to get adequate funding for a project they will definitely find somebody to make it. There are lots of hungry companies out there! Sponsors are naturally reticent about parting with their money. They want to invest it and make it back. Some never take chances and only bet on the "sure" things. Some will take chances if one of their people really push the project hard.