I suggest you leave the ram alone. Upgrading from 3 to 4 gb of ram is a waste of money unless you've already sold your old ram for a fair price. You won't notice any difference in performance with 32 or 64 bit windows. Upgrade the power supply or video card instead. Your ps is only adequate for what you have now so a high end video card won't work, but many low to mid range cards might. I suggest the 6450 for value; some go for around $35-40 after rebate. I get all my newegg and frys rebates, but some take 3 months so you have to be patient. If you want to get the ram anyway, I suggest you check your current ram label for a make and model number and try to match it. Or order from crucial's website. They guarantee their ram to work.
according to your mobo specs from the link you provided, your mobo will only handle DDR2 memory, so DDR3 upgrade is out of the question unless you get a new mobo.....but i may be wrong.....just re-read your specs....and under memory upgrade, some say DDR3, some say DDR2, so not really sure which is right.
Also, if your board only has 2 dimm slots, how did you manage to get 3 GB ram? (unless you are running a 32 bit windows OS and have 4 GB installed, then it would read just over 3 GB i think)
That is some messed-up specs; I assume 'some' versions of your HP MOBO (ASUS Mfg) have both DDR2 and DDR3 slots. The simplest way to know is to run CPU-z - http://www.cpuid.com/softwares/cpu-z.html and look at the 'SPD' and examine ALL slots 1-4 (see below). Next IF you have a 32-bit OS then IF you add a total of 4GB you'll only be able to use 3.0GB~3.5GB so IMO it's not worth the expense and hassle IF your current RAM is working.
OEM BIOS don't allow any OC'ing of either the RAM nor CPU so DDR3-1333 2x2GB is the max, and as I said earlier you'll gain at best +0.5GB installing 2x2GB. In a 32-bit environment 3.0GB~3.5GB is the maximum due to the OS.
Further, the difference between DDR3-1333 and DDR3-1600 is very small. The best way to speed up your system is to spend the money on an SSD -- by far the slowest component is your HDD.