So you've started SI and you've looked over the tutorial (don't worry, it's short).
Here's some basic tips:

• Use the boost to get through! While boosting, you're invincible and much faster. The default key to boost is C.
  
• Don't tape the fire button down. When firing, your movement speed is reduced. The size of the reduction is based on the weight of your weapons (light, medium, heavy) indicated by the color of the icon (green, yellow, orange) respectively.
  
• Don't forget about your consumable. Most consumables are very effective at making life easier.
  
• Want fast-firing weapons? Take blasters instead of machine guns. They have good fire rate and much better DPS.

This is just a list of perks/software and my opinion on them. However, perks that state what they do are not listed. This list is also a work in progress, so not every perk is here.
Joy: A drone that follows your ship, healing it over time. B+
Fool's _______ Projectiles: Multiplies your projectiles with no apparent drawbacks. A
Fool's _______ Radial Projectiles: Multiplies your projectiles, but shoots the copies backwards. D
I-Can't-Remember-The-Name-Of-It Fuel: Description in-game: "You are what you eat, and that is a big deal.": Doubles the size of your ship and reduces your speed, but gives a decent boost to health. F-, It will end your run if you take it due to your bigger hitbox and where your weapons fire from also being farther apart.
Flea market Alpha-_: Takes away 8% health, but gives a large boost to another stat depending on the number here ^^. B
Hot Wings XL: Shoots a short ranged cone of fire in front of your ship, but can be multiplied by the 2nd and 3rd software listed Has pretty good damage. C
Supreme Burrito: Same as Hot Wings XL, but shoots behind you. C
Jabba: A drone that uses Supreme Burrito as its attack. C-
Fatal Attraction: Very similar to the My Reflection item from TBOI, causing your bullets to boomerang back to you. However, when you release the fire button, you repel your shots. Unfortunately, this perk usually really is fatal to you, not your enemies due to its inaccuracy. Thanks to an update (or maybe i was just unlucky the first few times i took it) Hot Wings XL, Supreme Burrito, and drones are now affected by this item! That means their shots have a massive (infinite?) lifetime, so taking them with this creates a gigantic flaming burrito-gas shotgun of doom. Unfortunately, it also now comes with a 30% penalty to fire rate, but the potential for Hot Wings XL and Supreme Burrito makes it more than worth it. Even better, if your shots are obscuring enemy bullets, this keeps your shots next to your ship. You can also use lasers to keep some continuous damage. Also goes well with Lord of the Piercings, allowing you to swing your bullets around you like a mace several times, doing lots of damage. V-Aggra helps more shots to hit for a deadlier shotgun. B.

• Don't visit Lost Lords until the only other level is the Overlord.
  
• The percentages that appear when you select a stage are how close you are to that thing, not the chance to encounter one. Look at different stages to compare the numbers and figure out where the merchants, factories, and Lost Lords are.