Scavenging corpses and environments in Prey turns up all sorts of cadavers and curios, but you can only squeeze so much of it into your default inventory. On top of that, your inventory has to hold ammo and weapons in addition to crafting supplies and other items. Recyclers are good for breaking items down. Using Neuromod upgrades, however, lets you increase your inventory size.
How to Increase Your Inventory Size
You'll need at least three Neuromod items to expand your inventory. Once you're ready, open your main menu and select the Engineer tab. Suit Modification I is the skill you're looking for, although it comes with a prerequisite: Repair I. Invest in Repair I, if you haven't already, then pull the trigger on Suit Modification I.
Investing in Suit Modification I expands your inventory slots to 60. Continue along that upgrade path and you'll eventually be able to purchase Suit Modification II and Suit Modification III, which stretches your pack to hold 77 and 96 items slots, respectively.
You'll need 13 Neuromods total to acquire all three Suit Modification advancements.
When to Increase Your Inventory Size
Although other upgrades such as Stamina may seem attractive, you'll only find more crafting ingredients, ammo, weapons, and alien organs harvested from corpses as you progress. Go for Suit Modification I as soon as possible, since you'll run out of space quickly in the early game, then block out Neuromods for Suit Modification II and Suit Modification III as you notice more items cropping up.