first of all, for the GPU is suggest getting the GTX650 ti which is the equivelent to the 560 and better in newer games, low power consumption, plus TXAA in a few games.
for the monitor, if can get a 20" u can get a 22" too and it is measured diagonally so in width it's only about 1-1.5 inch.
if u can fit a 20" i dont think u can say
"I JUST CANT FIT 1 MORE INCH"
most pc tables easily support that high monitor and if u r not using a PC table, desk for instance, its even better the stand is the same and it just takes about 1 inch more.
and for the resolution question, many times in games 1080p just dosent FEEL like it.
the xbox fakes a higher res. and while pc dosent fake it some games just dont take FULL advantage of the 1080p some games look more clear in 1080p, or maybe its just me.
and for the 10FPS frame hit, why dont just lower the resolution a bit in 1080p?
and u also watch movies right? they look GREAT in 1080p!!
if u already have a full HD tv that u watch all the movies in, then the 900p is just for gaming.
IF not then 1080p is the way to go, if your parents dont agree just throw in a few bucks yourself, it might be something to u but it will last for YEARS to come.
for gaming that all i hav to say is that your GPU cant handle all the games in 1080p with a minimum 30FPS. but again many games it can max out without AA so if u can 1080p gets my vote.