Mining is 10-15 times faster than panning for gold. It's the only sane way to get most of those rewards.
As part of the tutorial, everyone receives a free pickaxe that lasts for two hours. If you used this up or lost it due to a bug, simply create another PSN account and log into Home.
However, I strongly encourage you not to spend money at the Western Frontier since Digital Leisure is a deceitful company.
You get 10xp every time you strike gold, whether it's mining or panning.
You can get between 10-50 gold each strike while mining, usually around 15-20 though. You can get between 1-20 gold when panning, usually about 2-5 though.
The big difference to me is that it takes about 30 seconds to mine for gold and you have to actively do it. It takes about 10 seconds to pan for gold if you're actively doing it and 20 seconds if you just start panning and set the controller down. Plus the panning spawns are closer together.
If you care only about XP, panning is probably the quicker (and less effort) way to go. If you want to get gold faster, mining is the better bet.