You'll struggle to find a 19" screen on a notebook.
They are available, but very uncommon and expensive. I've even seen a 20.1" screen. However, larger than 17" isn't really feasible or easy to find.
Mainstream is 15" or 15.4" widescreen, gaming tends to be 17" widescreen.
If you're going to use it plugged in, battery life isn't an issue for you.
A gaming laptop's battery will be short anyway because of the powerful components.
By memory, do you mean RAM or HDD space?
RAM is fast temporary storage - more of it improves the PC's ability to multitask, helps games load faster and play more smoothly, and soon.
HDD space is storage, where programs and games are installed to, and where you store documents.
An 80Gb disk is standard, they now go up to 160Gb.
Look for a 7200rpm disk rather than a slower 5400rpm or 4200rpm, as games will load faster and the laptop will boot much quicker. Overall performance will also be better.
What games do you plan to play?