Play on normal difficulty.
Use the Boulder style, with this style, you will have extra HP, which is going to be useful, because you wont be buying any HP from the shops. To safe up gems, of course.
The best way of getting gems is by cashing in your combos.
An 8-12 combo gives you 100 gems.
Getting this small amount of combo is easy in any of the areas, so you can focus on getting combos from the very beginning.
For the upgrades, I recommend having the Gem Powered and Gem Attractor. Rebirth is also helpful when playing with Boulder style (+1HP and more upgrade options onwards)
I got this by the end of the fourth area (Limbo)
But you can also spend about 1000 gems for HP if you make it to the boss area with a good weapon and good upgrades, because the boss spawns loads of adds and you are going to be constantly hitting those 8-12 combos, which will net you 1000+ gems if you constantly hit and cash in those combos.