Pentium D GPU Question?

Hello all,

I recently got into PC gaming, which called for an upgrade of my PC. (AMD 5800k APU+HD6670 in Dual Graphics if you're interested).

Now, I would like to take my old PC, install a new graphics card, and give it to my 7 year old brother. The most intensive task he will be doing is playing Minecraft at 1366x768. What graphics card do you recommend? My budget is around $50 USD.
The specs of the old PC are as follows:

Intel Pentium D 940 (3.2 Ghz)
EVGA 8400 GS
ASUS P5VD2-MX SE
2GB DDR2 RAM (Mobo max)
Old WD 120GB SATA Drive
Win7 Home Premium (soon to be Win8 Pro)

I have already looked at these cards:
Sapphire AMD Radeon 6570:
EVGA NVIDIA GeForce GT 620:


Also, some other questions:

1. My mobo's max RAM limit is 2 GB, is that a hard limit or is there any way to modify that (Custom BIOS, etc)?
2. Does 64 vs 32 bit Windows really matter, since I only have 2 GB of RAM?

Thanks,
Dakota