Running Windows 7 currently on my living room/family PC with a Pentium 4 (HT), 2GB DDR1 Ram and a Radeon X600 (for aero) and it runs just fine
To the OP... More Ram will make a big difference in performance, try your local computer shop for old ram sticks pulled from abandoned PC's- we all keep lots of old ram around. I give them away for free to people who bring in old machines that they want to keep using but need a new hard drive, etc. If you bring you local computer fixer a box of donuts- he'll probably dig up more free ram than you can use
Try ebay or flea markets to find more RAM cheaply. Install W7 on an UNformatted HDD, the installation program will partition and format the disk for you. Use Driver Genius or similar to find the latest drivers for each system. Use Tune Up Utilities 2014 to speed up your system. There's a fully working trial (15 days). Consider installing W8.1 instead. I personally don't like it, but some people do. It appears to be faster than W7. There's a free trial you can downloat at MS.
This is generally true, but not always a whiz-bang sure fire speed booster in every case. On many machines into which I've added RAM, the marginal speed gain was small. It just depends. The best way to speed up your computer is stop all the junk from loading at startup using a program such as autoruns. On desktops, the only programs I set to run at startup are the firewall and antivirus. Portables I allow a few more to start to allow for machine bells and whistles, but those usually aren't resource hogs. Some are so you may want to play around with them. Although Windows 7 will run well on some older computers, it likely will never run as fast on them as it does on the newest machines. At some point you're going to get to the limit of what the old box can do. Keep in mind, the cheapest price is not always the best price. What you want is value ... most performance for your money. RAM is cheap; buy decent quality and make sure it matches your system's requirements and that you'll be able to actually access the additional RAM. Windows is a bit "odd" when it comes to that.
If you're staying with Win 7 32 bit then there's a good chance Vista 32 bit or possibly Xp drivers for older hardware will work As said above, swap the HD before trying Win 7 to avoid the pain of reinstalling XP if it goes belly up. Win 7 DVD ISOs are downloadable so you have 29 day 'trial' before commiting to buy
Or make an image of your XP system using Acronis True Image Home or some such. No need to swap HDDs, just have a disaster recovery plan. There are freeware image makers too I seem to recall. Research on this site, or the internet in general, can point you toward them. Forget running out and buying Windows 7. You can download virgin Windows 7 (media refresh version) via links provided by this site. They're untouched and assuming you get no errors when downloading (verify the download) or burning (burn at slowest speed) you'll get a "Microsoft-quality" install disk. And this site can also give you extremely good instruction on activation of the OS after installation. If you later feel you just gotta be genuine, you can always buy a license and apply the key to your MDL-gotten Windows 7 installation.