In my opinion, Jets'n'Guns is rather easy on Normal difficulty, you just do not get enough challenge in your first run, and the subsequent playthrough will be a bit boring with the Hexagun and the entire high-level arsenal. Hard difficulty means you will die more often, but beating a level will bring much more satisfaction :)

My advice: use Autotrack Miniguns !
Daisycutters and Superkillers may have a higher dps, but shooting straight forward means taking return fire in the face or losing at least half of dps due to evasive maneuvers. Autotracks allow you to land fire constantly while maneuvering. The main trick with Autotracks is that you really have to AIM them. If you just fly in the corner of the screen, most shots will miss the targets. It can’t fire ahead of fast-moving enemies. Always position your ship almost at the same line with an enemy, just a bit higher or lower to avoid its return shots.
Autotrack Minigun is cheap to purchase and upgrade, you can quickly buy 3-4 and spend all excess money on Autotron AIR, Phoenix missiles, Rodeo missiles or just ships and upgrades, whatever is good for an upcoming mission.

Some advice on upper levels weaponry :
Levels 1-19 – use 2-4 Autotrack Miniguns, replace one with Superkiller if you really need some forward firepower. In jetpack missions use Skywalker Hypergun, Superkiller Mk.I or VX-MB Laser. Swarm is just too expensive and hot to replace the Miniguns and can’t effectively kill fast targets. Alternatively, you can buy Rotary Cage and rotate forward-firing guns, but I'm just lazy for that.
Levels 20-25 – replace one Autotrack Minigun with fully upgraded Zombie Blues PG.
Level 26-27 – try to get Zion Wave Emitter and replace one Autotrack Minigun with it.
Level 28+ - welcome NTR Sandman Laser!
Level 35+ – don’t forget to equip Hexagun.

Have fun!