The tone is mostly a combination of the amp, speakers and pickups on the guitar. Followed by that are a lot of other things like room acoustics, string guage, wood type on the guitar, the state that the tubes are in, cables..etc.
Then there's the whole recording side of things with boards, compressors, bit rate...and so on..
What I'd probably do is start with the cheapest solutions first and work my way up the list. So cheapest on that list is just change the room acoustics. Move the amp, maybe build a cheap 'booth' made out of insulating blankets to place around the amp if recording is your main goal. Try moving the amp into the corner of a room and use that as a bass trap to add more bottom end. If you get too much bottom end, move the amp off the floor.
If that doesn't help any, then I'd just start trying the other lower stuff on the list like changing the strings, using some decent cables, get new tubes.
If that doesn't work then it's time to start thinking about major changes like your speakers.. like, is it better to go 4X10, 2X12, Closed-Back, Open-Back, Vented.
If that doesn't work then just either admit defeat and get a new amp or consider making changes to the guitar like new pickups.
Another solution, is to stick with what you have and use a decent overdrive pedal, compressor or EQ.
If you have the cash, get yourself a decent multi-effects unit and you'll never have to worry about the sound again. Some purists argue against it, but I've always been a big fan of them and use a GT-8 and Amplitube all the time.
Hope that helps. :)