What can i install in my 03 eclipse to up the horsepower?

It depends on that the stock internals can handle. I dont know it off the top of my head but it can be easily found. If you go with a small turbo and run lowish boost theres a good chance the engine can handle it with just an ecu map.

Could I upgrade the internals to handle a bigger turbo?

to upgrade the internals you would have to do rods and pistons that are stronger and would lower your compression. you would probably also have to put in an upgraded head gasket and upgraded head bolts/studs to do it right. after the internals you would need all the plumbing, im pretty sure that someone makes turbo conversion kits for eclipses. you would need to also upgrade your fueling and get a new ecu tune to do it right. honestly a turbo sounds liema fun project, but to do it right you are looking at a lot of money. if i were you i would start out with just an intake and exhaust for starters just to see where that gets you. also one top of that, make sure the car is running like a top before you even consider getting into turbo upgrading

So would it be easyer to get a completely new engine? If so which one would work best for my 03 eclipse gs?

it depends on what direction you want to go in. if you wanted to do a fairly easy motor swap to make the car turbo ready you could try and grab an engine from either an eclipse gsx or a 3000gt vr4. both came turbo'd and i think either one is a direct bolt up. keep in mind though that engines are expensive and you would still want to get either one running nice before doing any big upgrades which is something that would have to be done, guaranteed considering either engines are from older cars. having said all that it might just be easier to build up your current engine, but like i said, it all depends on which direction YOU would want to go. i suggest doing some research. go on mitsubishi forums and ask the pros and do some Wikipedia reading and then you can make an educated decision for yourself. good luck and let me know what you decide

Will a stock turbo be to much for a motor that didn't come turbo

how much horse power can you put in a Mitsubishi 2001 eclipse

Guys if you want to add some small turbo without any modificationsthis will add max 10 hrspr so instead change the air intak this wil add some 8 hp and the exhaust will add some 3 hp this will help you to get a 220 hp on your eclipse