I will start by saying everyone has their own opinion, and everybody wants different things from their car.
In response to some of the posts in this thread:
If you JUST increase the engine's power, yes in a straight line you will accomplish the same acceleration as a car with a corresponding amount of weight reduction. However, when it comes to slowing down or turning (ceteris paribus) there will be a big advantage for the lighter car. There are lots of other advantages to weight reduction also, fuel efficiency and less stress/wear on components being just two examples. I'm not saying anything bad about increasing an engine's hp or tq output, I'm simply defending weight reduction.
People have mentioned noise, comfort, etc. That's where each situation will be different, because different people want different things. The same goes for factory built cars, one person will think a car is comfy, and a different person will think it is not. There is no definitive answer because it is all relative to what the individual wants.
You shouldn't blame weight reduction for making you lose traction. If you're tires are no longer gripping as well then the tire setup has become a weak link. You don't see people blame a large turbo for traction issues. They understand that with their current setup in the current situation the tires are being pushed past their limit. You can still change suspension, the car's balance, apply downforce, and other things without even having to change the tires. But instead, you put the weight back, slowed the car down lowering the g-force and got traction back. The weight reduction wasn't the problem, it just showed you that your tires are right on the edge of grip. Any modification that increases the force on the tire by the same amount will have the same effect. If you want to put the stuff back that's fine, like I said everyone wants something different, but don't blame it for making you lose traction like it did something wrong. Obviously with a LOT of weight reduction the car will have to be adjusted accordingly, with changes to suspension, alignment, etc.
You can't compare a FR to a FF car, yes we are front heavy but that is like comparing apples to pears.
There are lots of good suggestions in this thread and by searching you will find a TON more. But what it will really come down to is what YOU are comfortable removing. You also have to realize that if you are going past the point of no return, you have to take into consideration you probably would not be able to sell the car in the future. At least not for a price you would think is reasonable. Unless you can find someone that wants to buy the car and wants the exact same things as you. However this goes with any kind of personalizing to an automobile.
With that aside, don't let someone else decide wether or not YOU want interior, or air conditioning, or heat, etc. YOU are the only one that can decide what you can and can't live without and what you will or won't need in the future.
As others have pointed out there is also weight reduction you can do that can't even be seen. The aluminum driveshaft and flywheel are good examples. Reducing rotational mass will also help get more power to the ground. There are lots of other items that can be replaced by lighter ones. The stock seats are a good example. The stock hood is also heavy, stock rims are heavy, etc.
I wouldn't recommend lexan unless you've already done a lot of other weight reduction. It was a lot of work for the small gain and I didn't even have to worry about making it water-proof.
Since you're just starting out you have a lot of options, however please keep safety as the #1 priority, for both you and others around you.