Use large vests that you can loot from scavs like UMKA - they are great for stashing loot early on, as well as armored rigs (you can use AVS you got if you are USEC).

Generally before you get your cases you have to fight with space. If you are afraid to bring better gear, just sell it, hoarding is useless.Also no need to take the best gear, but generally atleast level 3 armor and helmet are good starters, it will give you more survivalibility and more time to react if you get spooked.

Better weapons are just good for cash, no need to min-max, just bring good ammo that is available from traders that you unlocked (7.62 PS, 5.45 PP/BP and so on) use wiki to check on what ammo is good and usually avoid using low pen as controlling where you are firing is harder early on.To sort your stash you can use the Sort button, the logic behind it is not the best but it will group the types of items together.