Your biggest issue is going to be fuel management and ecu tuning,depending on how hard the ecu is to crack. DI is also a relatively new technology, what we do know is you can run higher C/R due to much more accurrate and cleaner fuel burn directly into the combustion chambers. Hard part is you better hope that the stock Injectors can handle an increased fuel demand.
On my Mazdaspeed3 with a 2.3L DISI it has a 9.5:1 C/R that puts out 256/280 hp/torque. Not bad for a 4banger. It took about a year to get anytype of tuning out as well as fuel upgrades. However, one of the first modifications to help with the fuel problems and detonation was methanol injection. You will aslo probably want to change your plugs out for 1 or 2degree colder plugs and run on 93 octane. You will get huge power from going turbo. I'd put pricing for a kit at around 4500 minimum for a single turbo setup. More than likely going to come with a enginemanagement of some sort,turbo, turbo manifold, downpipe, intercooler, piping, possibly fuel upgrades, and various hoses,fittings,and clamps.