I still don't know if your basement is poured yet, or not. IF it is, I'd still suggest you NOT jack it out to put in a piped system, hence, it's moot as to what type of pipe is used (if you know what I'm saying). It just seems like more work than it's worth. This is where B-Dry and such come in handy for (potentially) leaking basements. And again, if you want to do more, you can look at all the outside items I described, and go as far as putting in a 'system' out there.
For basements being poured, rigid PVC is used, usually with cross-laterals every 10'. The rigid withstands the concrete's weight and such. If the interior OR exterior system uses filter fabric, then you can pump the water right out because it's, well, filtered. If the system being installed as you want uses a sump pump and it DOESN'T use some type of filter (whether it be fabric or not), the pump may fail a lot sooner than you'd like. Do consider a batter backup for your pump.
As usual, if you have more to ask, go right ahead. My best to ya and hope this helps.