Home Server for an iOS developer | Xcode continuous integration
A late-model, mid-range  Mini will be fine. If all you need is a personal webserver and compiler farm it's very good value. Probably not powerful enough for rendering 3D animation unless you're patient.

Your storage concerns are very easily eliminated by plugging in an external drive. Get a small SSD with the Mini, store your stuff on a FW800 or Thunderbolt external. note that if you offload your storage to an external there is no point in getting a fusion drive.

Don't forget backups, but do hook up the backup drive via USB2. Simple hardware throttling keeps the backups running at low priority.

I have a 27 inch iMac running Server, it has no problems whatsoever keeping up with the load. I could not do my job as well with a laptop-size monitor but I don't think I'd notice laptop performance.