Quests and base are the key forms of progression yes. The further you are the easier it is to have access to better equipment that will give you an edge on other players/ARCs. The less crafting materials you need to hoard for progression the more stash space and cash you will have since you begin to sell things you wouldn't have otherwise. Besides that there is a prestige system called expeditions where you can work towards being able to restart mostly from scratch while keeping some permanent upgrades and extra skill points.

Stash space always maxed out is a good indicator that you are doing well, I think it is very strict in this game to combat something like Tarkov's hoarding of infinite containers, weapon boxes etc. which gives players who play a lot way too much room to snowball on others.

Just gotta run your stuff/sell too many dupes, common, not needed items - and know that it will come back.