Not sure whether it would be suitable for a core/hybrid, hopefully somebody else will be able to tell you that (I would have thought so mind, make sure you get a second NIC sorted though). Do you intend on running other MDs off it? If so, maybe considering getting the miniITX now as a hybrid, then get a normal desktop for your core with a bit more grunt at a later date when funds permit. The miniITX can then be used as an MD.
With regards to your PSU question, some cases have them included, but this is reflected in the cost. If you don't care about bulkiness, then just use any old PSU that you may have laying around, or pick one up nice and cheap. Personally, I have built my own case for my miniITX board, and have sourced a 1U PSU off ebay so everything stays nice and thin - the whole lot is then bolted to the back of my TV via the VESA mount. They are very, very cheap (£15 for 180W!), and do a good job of powering the system. That said, I am using my miniITX mobo as an MD, not a core/hybrid (but get one with sufficient power output, and I'm sure that'll be fine).