Interestingly enough I've had all four!!! My first car was a Corolla - hated it. Second car was a Honda Accord (not a Civic, but close enough), and my last car before the P5 was an Integra, which I actually did love.
When I started shopping for a new car I test drove EVERYTHING. It took me two months to make a decision because I was really confused by all the different options. All around, however, the P5 couldn't be beat. I mean that in as unbiased a way as possible.
For the price you pay, you get so much - 130 horsepower, 16" alloys versus 15" hub caps, the nice styling which already looks aftermarket, good suspension, etc., etc... You can get the Honda and Acura to have as much stuff as the P5, but only after you pay a lot more money. What you should do is look at what you get for a certain price accross the board. Otherwise, you're comparing apples and oranges.
Both my Honda and Acura got stolen, believe it or not, because I had so much done to them that people could easily strip them down for parts and have a million buyers. Not so with my P5- good luck finding many buyers for those parts when hardly anyone has one yet! I feel safer about spending money on it, but I guess you'll only care about this if you plan to fix it up.
About the Corolla, if it's free and paid for, that might be something to consider as a temporary choice... It's always nice not to have a car payment.