Simply removing the catalytic converter without upgrading the piping and exhaust manifold won't produce any noticeable gains, apart from perhaps a placebo affect, lol. You'll also have to check to see if it's legal where you live too. I noticed a minor gain in power when I removed my catalytic converter, but I also installed aftermarket headers at the same time. The power increase was more noticeable when I upgraded the exhaust piping to 2" and added a high-flow muffler. If it's not legal to remove your cat where you live, then just go for a cat-back system instead, with a high-flow cat in place of the original one.
Upgrading the exhaust piping size after removing the catalytic converter often results in the exhaust note sounding raspy, as the cat acts like a large resonator. It's a simple fix however as you can just add extra resonators in to get the tone you're after. I tried quite a few different resonators on my 7th Gen Corolla when I installed my exhaust as I couldn't stand the raspiness and loudness (the before and after videos are on YouTube). A couple of resonators later (one 18" and one 10") the raspiness/annoying droning was gone and it's nice and quiet until I put my foot down.
As for adding the CAI, it will increase power, but don't expect very noticeable results. It's better than a SRI and you'll gain top end power, but will lose a tiny bit of low end power as a result. They're both great mods to do as they increase power and look/sound good, but just don't go into it with high hopes of getting highly noticeable results