For basic web surfing/word processing, the i3 will be just fine. There is no need for anything more than 2 cores for those kind of things. Also, the i3 is actually a decent CPU for gaming, it's not the best out there, but will still work. The i3 benchmarks that i have seen are equivalent to higher-end Core 2 Duo's and there are still PLENTY of people using Core 2 Duo's for gaming.
As for RAM, that all depends on what operating system you have. If you are using a 32-bit OS, then the PC will not be able to utilize more than 4GB (keeping in mind that on-board system memory is used first), so if you have 4GB of RAM in a 32-bit operating system, the operating system will count video card memory, any on-board controller memory first, then it will allocate the rest of the RAM up to 4GB.
Example:
32-bit OS only supports 4GB of RAM, start with 4GB and keep deducting...
-video card has 1GB of RAM on it, this leaves you with 3GB or RAM that the OS can use
-on-board controllers for various resources like controllers and other things take up 512meg of RAM, this leaves you with 2.5GB of RAM that the OS can use.
out of the 4GB that you install, only 2.5GB is allocated for use, the rest is dormant thus wasting 1.5GB of RAM.
So, if using a 32-bit operating system, only use 2GB of RAM
If using 64-bit operating system, you can use 4GB or more if you desire, but you should really need no more than 4GB of RAM for basic computing.
Now, if you decide to get an i5 or i7 PC, it'll perform better in many things, but you will really not see the difference in basic stuff like web surfing/Word Processing, but, if you decide you want to play games or do video encoding, it will benefit you. Also, the i5/i7 PC will be more future-proof and likely last much longer than the i3 PC.