Oh, I envy you for being able to play SS2 for the first time, I really do. Still love it and it's one of my all-time favourites and I play a lot of games new and old.

Usually you don't need to haul all the stuff. E.g. with the research the ingredients you can usually just leave hanging and return for them later when you need them. Also depending on your focus you don't even need all the weapons, good starter is having the small weapons with you and maybe later on replacing the wrench with certain other object that you'll find. Also carrying multiple armors or the bio-hazard suit is unnecessary unless you really need to go somewhere with the latter. Also chips and drinks are better just eaten immediately.

Later on you might find a handy device that'll help you with clutter, but until then it's best to just go with necessary stuff. Weapons, ammo, healing stuff, maybe antitoxins and rad hypos. Also if you find games, insert them into the game console so they don't take up too much space. There's also no need for multiple same software upgrades so those can be ditched. I generally apply them since they make a nice sound though. ;)

What else.. brawnboost implant is nice, but remember to keep it loaded. Same applies to the certain armor you might find later on, I personally don't really use it due to the battery limitation.

In a nutshell, you don't need everything. Use guns you have skills for, with specialization you can use the better ones.