Gaming:
Gaming on Linux has improved, but it's still mostly crap. I've tested that out extensively.
Most Linux games I've found with SteamOS (so not using WINE) were roughly 70% of the FPS compared to Windows. Within that group of games that "worked" several had issues such as stuttering.
(You don't want STEAMOS. That's just based on Debian I believe, but you can put Steam on different Linux distros and have it download Linux games. Provided the video drivers have been installed STEAMOS and Steam on Linux should work the same in terms of game performance, however STEAMOS is useless for watching your own videos or do other stuff. It's locked down so you can't download applications very easily.)
*Your gaming performance on Windows may be primarily the GPU (iGPU or graphics card). No idea, but even with the 3GB of system memory, an okay CPU and okay GPU there are a few games that would run fairly well.
64-bit stuff:
(whether you can use 64-bit Operating System depends on the CPU; easy to check if you are uncertain)
It's largely a non-issue unless you have a graphics card that has more than 1GB of VRAM. The main difference that 64-bit x86 offers is more addressable memory.
32-bit can address a 4GB memory map. This includes the video memory, system memory, and some minor other things. Basically, just take 4096MB (4GB) and subtract 200MB, and subtract the size of VRAM and you're left with the amount of system memory that the system is capable of addressing.
For example, if you bought a 2GB video card, despite having 3GB of system memory (DDR2?) installed you would only be able to use about 1.8GB of it.
So...
Here's an example of a Linux start:
1. Linux Mint 64-bit (if CPU supports)
https://linuxmint.com/download.php
2. Burn to USB. i.e. use RUFUS https://rufus.akeo.ie/
3. hit "DEL" on startup to go into BIOS, then look for BOOT ORDER and change so USB HDD or similar is first.
(if super stuck you can keep the computer off and just DISCONNECT the HDD cables from the rear of it. The computer will then look for the next bootable device. If it's capable of doing USB, and the USB was done correctly with RUFUS it should start the bootup)
4. Boot to Linux Mint, create user name/password (write it down)
5. test.
6. GAMES is a separate post really, but STEAM (not STEAMOS but just install Steam) may be the way to go. You'd have to ask carefully though for what games work with your older hardware. Usually older 2D style games work best.
Microsoft's Age of Empires series for example?