Short ram might still be worth it - heat soak is your main enemy there. Once the car is under way, the outside ambient and underhood temps are pretty close together. With a CAI, depending on where you live, hydrolock is a possibility. Modifying the stock intake is a mixed bag - some have gotten similar power gains of a CAI by removing the stock resonator (behind the bumper cover, between the fender and wheel well) and dropping in a free flow panel filter. Atleast it makes the same sort of noise as an aftermarket intake.
Adding a piggyback might be worthwhile - will need to find one that can control the VVT-i to get any appreciable gains. That means something like a CAMCON or similar. Problem is, these are non-trivial to tune. Unless you can find a garage to help you tune this - it would be a matter of you street tuning it, trail and error. This would also mean adding a wideband O2 sensor to help you tune it. The factory tune is pretty conservative. Optimizing it with a piggyback might yield 5+ HP gain.
The classic I/H/E (intake / headers / exhaust) doesn't generate decent gains on the 1ZZ-FE, as it is already pretty optimized. The exhaust manifold is already a tubular design - some Celica guys were able to port and polish it and get a couple of HP gain. Surprisingly, just bolting on a TRD muffler made a decent jump in power ~ 5HP. But that was on a Celica - same basic engine, but they have a different tune, different setup of intake and exhaust, and slightly oversized valves in the head. In case you were curious, yes, there were a number of owners that move the Celica GT ECM and intake/exhaust to a Corolla - gains achieved was basically zero. Intake mods are a mixed bag as well. Some have reported good results with a composite shorter length runner design of the 9th gen intake with their larger throttle bodies. Not a huge amount of power, couple of HP, but the real gains were in throttle response. The car sound and "felt" like it had more power.
Tune for I/H/E + piggyback - maybe look at 10HP gain, possibly more. The engine is just too optimized to get a lot from bolt-ons.
To really unlock some power, need to crack open up the engine. Aftermarket cams have shown good results for the least amount of work on the engine. Coupled with a good intake / header / exhaust + EMS - could be realistically looking at 20+HP gain. But at that point - might as well strip down the whole engine and rebuild it with higher CR pistons, P&P, etc. - go all out N/A. Or go the other directions and pump money into a forced induction project. Cheapest way to get more go is to go nitrous. Can always do a swap as well - couple of interesting possibilities - depends on amount of money and time you want to put into it.
The 1ZZ-FE is a great engine - but to get any tangible gains - you need to spend some serious amount of money on it.