Rega P2 setup - high end newbie

Hi! What a great site (with great forums). I did a lot of research before shelling out the big bucks (relatively speaking) for a nice turn table, and this forum was invaluable. I have a question for anyone that will answer about balancing a tone arm.

I just bought a Rega P2 with a Grado cartridge (does it matter which kind?). It was balanced at the store I bought it from, but when I took it home I couldn't help but rebalance the tone arm so I could understand exactly what was going on. So I leveled the record player with bubble level, then put the anti-skate to zero. I then balanced the tone arm at 0 (the arm is floating over the record surface). Problem is it always floats back to the tone arm rest... Anyways, I then adjusted the weight to 1.5 grams (a three quarter turn) and put anti-skate at 1.5.

So, my question, is there any reason other than leveling innacuracies that would make my tone arm always float to the right towards the tone arm rest (away from the record), and is this something I should be worried about?

Also, When I have the music at a decent level, when the record gets to the last track or so, there's an audible humming. I'm assuming this is the motor. Is this normal? And lastly, my tt squeaks on start-up. It's not really an issue, but is this also normal?

Thanks for any help you can offer!!!

Yes, the tonearm floating away from the center is from the anti-skate mechanism. Don't worry about it.

Regarding the hum, this is common with Rega and Grado. Check the archives about solutions. Other cartridges do not exhibit this humming.

Squeak on startup may be belt tension related.
Twl is right on point. I would add that the combination of the Grado and the Rega could be best described as unshielded cartridge meets unshielded turntable motor. Grado is famous for this problem. There may be inexpensive mods for your turntable to give the motor some shielding and eliminate the hum.