done paint work on pc many times, since its a new inside you wont need to do much prep work. you should not have any problems painting all visible corners of the inside of your case with spray paint.
The best way if you dont want to get anything wrong or messy is to take it to your local body shop garage and and ask for one of thier standard colours to be painted on your case, this should be cheaper and time saving than you doing it on your own.
Make sure you remove all plastic, and metal that is not going to be sprayed, pry off anything that is glued with a glue gun, (you will need to use a glue gun to stick it back on) then use masking tape and newspaper to tidily cover all the parts that you do not want painted.
you can ruff up the surface very lightly at firs if you want with very fine sand paper, i believe its over a 180 grid, in aluminium oxide. (however since its new you dont really have to)
When spraying make sure you get familiar with the pray can on a tes surface, so you dont run the paint or spray to light.
You need to lightly spray primer, dark primer for black paints or getting a rich solid colour. and white , silver primer for lighter colors to get out the brightness, shine.
after a light prime, u need to use grit paper lightly to (around 300) get of any of those flakes if any or any uneven dots. (how ever this isnt necessary again since its the inside of your case, cos you wont be running your hand against the paint work)
apply a second coat of primer after an hour. if your in a cold or damp place then after 6 hours.
now you should have a even primed base to hold on your main pint.
If your going for mat to will need three coats of matt paint evenly distributed.
However i do not recommend using matt, i would say to use gloss instead, great colors are lime green and Chevy orange.
If you are using gloss, liquid base or double acrylic, you should use 4 coats at least.
each coat should have 30 minutes to set.
after the colour coat at least 3 coats of lacquer should be sprayed.
again if you want peace of mind you local body shop would do it for 3/4 of the price you would spend doing it yourself. and go for gloss, trust me