Welcome to the site and nice ride. Yellow MP3 FTW
First of all, you have a P5 exhaust. The tip doesn't come out far enough and it's causing your rear lip to build up all sorts of soot and crap. Get a sedan exhaust before anything. The only thing you NEED is the axleback/muffler portion.. ALL the rest of the exhaust is the same between the hatchback P5 and the sedans (MP3/MSP/etc).
Second of all, your battery doesn't look very secure. Did that bolt snap? Try to drill it back out or something so you can secure the battery.. you don't want it sloshing around and moving while cornering.
As for power, that's gonna be a challenge. There is no "cheap" aftermarket turbo kit available.. actually I don't know if there are any complete kits available anymore (none that I would personally trust anyway). Your best bet will be to source all the parts individually and build your own turbo kit. There is no need to swap the Mazdaspeed motor because it's the exact same engine as what's in your MP3. The only difference is the presence of an oil cooler and a turbo.. that's it.
Another thing to keep in mind if you're serious about this turbo business is that the MP3 ECU is special in that it has advanced timing which gives it a bit more power than other NA Proteges (use 91 octane or higher because of this.. follow that sticker by the gas cap). However, this is bad for turbo engines.. so you'll want to invest in either A) Some fort of fuel management that allows you to control timing or B) A Mazdaspeed Protege (MSP) ECU. Option B is much easier, but there's a problem with that option as well.
The problem you'll encounter is that the MP3 doesn't have VTCS flaps in the intake manifold, so the wiring for the VTCS solenoid was never installed in the MP3. However the MSP DID have the VTCS system, so the ECU from the MSP is going to want to see the VTCS solenoid plugged in or else your car will have a CEL and run like ass on cold starts. See this thread for details on how to fix it.
http://www.mazdas247.com/forum/showthread.php?t=123748013
Other than that, it's just another standard turbo build. You'll need a turbo manifold, turbo, oil/coolant lines, downpipe, intercooler, pipes, intake, blow-off/bypass valve, gauges, and other little things. I turbo'd my MP3 for around $2500 using the Mazdaspeed Protege turbo. It adds up fast, so get ready for it if you're serious about making this car fast.
Oh and ditch those steelies man.. I hope the previous owner at least had some other wheels to go with it. Please say yes..