IMO, don't buy fiberglass insulation after spending what you're going to spend on the basement remodel.
At a MINIMUM I would suggest using Roxul Safe n' Sound.... Stone Wool insulation, great noise cancelling, you wont be all itchy, cuts with a serrated knife like a saw through wood so you can sculpt it to fit spaces better, etc... It's friction fit and should stay between the joists just fine, but if needed you can put the little rods across the joists to hold it....
Another bonus is Roxul is essentially fireproof. I've put a flame from my mapp gas torch against it and it doesn't ignite...
Roxul Safe 'n' Sound 3 in. x 15-1/4 in. x 47 in. Soundproofing Stone Wool Insulation (12 pieces / package)-RXSS31525 at The Home Depot
For even better results you could do a flash n' fill where you spray the cavity with a layer of spray foam, and then fill it with roxul on top of that....
Dual Purpose Open Cell Foam Kits
That kit is open cell, if you need it to also be a vapor barrier then get closed cell stuff... More expensive but the amount of time spent working is cut by a HUGE margin. In my parents basement we did closed cell foam on all walls, then roxul in all the celiing cavities and couldn't be happier with the results...