While there are ways you can upgrade your existing system, it's alays worth remembering that
wanting to build something new is a good reason to do it
that said:
It'd be even better to see if you can find an Athlon II X3 or X4. A quick check on task manager shows each
tab I have open in Chrome is running multiple threads; most have 14 threads spawned, and one has 48! I have 18 tabs open, which means that Chrome alone is running ~ 20 processes and handling 200+ threads. Multi-tab browsing needs to be looked at as multitasking; more cores will help. I've just had a quick check and your board is apparently "optimised" for AM3 processors, so you should be good to go
Also, if your 4GB of RAM is in 2 sticks, you've got a couple of free RAM slots so you could easily double the RAM to 8GB. In fact, personally, I'd look at upgrading the RAM *before* I thought about getting an SSD - the SSD will make things load quicker; more RAM will help everything to run more smoothly.