The issue with the A6300 is that it only has two memory slots and can only take 2 x 2GB of RAM for a total of 4 GB. Pretty low by todays standards, but still workable. Cheap upgrade too.
CPU is still one of the in-between processors that HP used, however it is nestled in a slot 775, which means it can take a Core 2 Duo E8xxx or E6xxx CPU.
All that said, I think I'm going to agree with pconroy though, invest in a new computer. If you did upgrade to 4GB of RAM, it might be okay for now, but you'll soon figure out you'll want more. However, cheap upgrade. It would be around $30-35 to max out the memory. 32 bit OS will see about 3.5 GB of it, the rest would be dedicated to motherboard and video addressing.
As for comparing old to new, while Moore's law is still proving to be true, the actual speed of the processors is leveling off. The way they gain speed now is with more internal cache and more cores on the CPU. When it comes to 99% of what the average user does, they wouldn't notice much of a difference between a 2008 Core 2 Q68xx processor and todays i5. I actually downgraded one user that was having problems with their i7 PC down to a Core2 and they told me about a week later that it seemed faster. Ha!
CPU speeds went from 1 Mhz to 4 Ghz in a relatively short period of time, but then they started going backwards. Common speeds now are typically right around 3 Ghz. Again, caching, efficiency and multi-cores are making up for it.