I already have a computer and plan on upgrading it. I have a Pentium 4 3.0ghz which is in an Antec Sonata II case which already had a power supply (I am pretty positive it is a SmartPower 2.0 450W ATX12V)
I already like the case and do not plan on changing it unless I have to.
the case supports mATX MB's so you are ok there. the PSU probably isn't going to hold the core i3, though it may. you would need to research the PSU a little and see what the specs are. Personally I would just replace it with a ANTEC ECO 520W rather than risking frying your new parts.
Currently I am using almost that same case the Antec Sonata Pronto RT, I like its simple design and good space. As far as power goes take a look at this tool http://extreme.outervision.com/psucalculatorlite.jsp. It will give you an idea on what you need for a power supply on a low end. I am using a 500 watt power supply with a Intel® Core™ I7 2600K (not overclocked at this time) and not having a problem with it.