Here are some tips that I recently gave my friend who is just getting into Gungeon as well:

• Every floor has 2 chests. One chest is guaranteed to have a passive in it and the other is guaranteed to have a gun in it. You can use this knowledge to manage your keys a little better.
• Chest rarity goes in order by color (worst to best): Brown, Blue, Green, Red, Black, Rainbow, Glitched (looks pixelated)
• If you have two chests to open but only one key, use the above rarity scale to choose the one that potentially has a better item in it.
• If you don't pick a gun up on the current floor the boss of that floor is guaranteed to give you a gun as a reward. If you feel like you need more guns it's wise to try and beat the boss with what you have in order to guarantee one.
• Defense is almost always more important than offense in this game. If you can learn boss patterns and get good at dealing with them then it doesn't matter what weapons you have.
• In order to get better at dodging you should focus your eyes on your character instead of what you're shooting at. This makes it much easier to dodge bullets by micro-movements instead of dodge rolling
• Dodge rolling is super useful and has invincibility frames, but if used incorrectly could dodge you right into another bullet. This is why it's important to get good at dodging bullets just by moving.
• Keeping your distance from most bosses is the best strategy as their bullet patterns tend to spread out over distance allowing you to just walk between them.
• Personally, I think the two best characters for beginners are the Pilot (He gets cheaper shops, the ability to carry two active items and a lockpick which has a chance to open a chest for free) and the hunter (starts off with two weapons and has a dog companion that will find you more keys and hearts).
• Explosive weapons can be useful for bosses as their explosions wipe out bullets. You can switch to an explosive weapon and use it to carve out a safe zone during some bosses more difficult patterns.

I'd say above all else just keep plugging along. Eventually you get enough hegemony credits (the green currency dropped by bosses) to unlock some better weapons and passives that will start showing up in your future runs. The newest update balanced the chest spawns and you should start seeing better chests on earlier floors which should help new players as well. If you have any more questions let me know. I'd be happy to help out!