Equipment slots hold the equipment you are currently using; most of it is advantageous for one reason or another.
Your go-to weapon for engaging enemies at a distance. Unfortunately, most enemies prefer to close in and attack, but this opening salvo can end a fight before it starts if your enemy doesn't have one and you do. In most cases, your LRW will only help you once per fight; however, some scenarios will involve you making much more frequent use of this. LRWs often come with modifications to increase fire rate (for example, Three-Round Burst lets the weapon fire three times at diminishing accuracy, and Spray-n-Pray fires a whopping ten times with a fairly low accuracy).
Your most commonly-used piece of equipment, short-range weapons give you what you need to kill people. You may occasionally have to swap them out in mid-combat - say, if your existing weapon runs out of power (thus becoming a very shiny club), is ineffective, is knocked out of your hands, or something better comes along.
Never underestimate the power of a good set of body armor. Body armor reduces damage by a percentage, in exchange for losing its own HP. Typically, body armor's percentage damage relates in part to its ability to cover - a skimpy bikini made of Invincibilium may have insanely high hit points, but almost never actually block anything, for example. The strength of body armor (and whether it is actually helping protect you) has some mitigating factors towards whether you suffer critical wounds to vital areas.
The most important reason to have a helmet is to avoid taking severe damage from critical headshots. However, in addition to armor protection, helmets can also provide HUDLink capability - letting your personal computer and other items link up to it to let you use them in the middle of combat instead of digging them out of your inventory, and sharing information that would normally require tedious menu-manipulation.
While shields aren't exactly the end-all be-all of defensive technology, anything that puts a barrier between you and death is worth it. They usually have a low deflection bonus and a high amount of damageability, and better, can be replaced with relative ease. Always keep one handy.
You're going to be spending a long time on your feet, so you may as well have the best boots you can find. Boots give minimal armor bonuses, but the most important benefit of boots is to reduce fatigue and other negative effects from walking.
Your backpack is what lets you carry more stuff; without it, you're vastly limited in what you can haul around the wastelands. A better storage unit is always a wise investment.
The CyberGlove is a computer system that is worn on the right hand and arm, typically used to augment combat capabilities, determine weather, connect to heads-up displays, interface with systems, and generally make life easier.
Equipment can receive upgrades to be more impressive than usual.
Accurize: Increases weapon accuracy. 10% for 100% cost, 20% for 300% cost, 30% for 500% cost.
Intensify: Increases weapon damage. Cost as Accurize.
Universal Ammo: Weapon can use any energy ammunition at 100% efficiency. 300%.
Stunner: LR weapons only. If successful, enemy cannot act for first few melee rounds. 400%.
Three-Round Burst: LR weapon fires three rounds. Acc 100% on first shot, 80% on second, 60% on third. 500%.
Shockwave Blaster: LR weapon may knock random item out of enemy inventory or equipment slot (15% chance.) 400%.
Grenade Launcher: LR weapon can fire grenades in support as well as normal attack (30% acc penalty). 400%.
Armor Burner: SR weapons burn through armor faster. 200% boost = 75% cost, 300% = 150%, 400% = 225%, 500% = 300%, 600% = 375%, 700% = 450%, 800% = 525%.
Deathpulse: SR weapon may inflict 5 to 10x normal damage; uses more ammo and breaks weapon much faster. 500%.
Armor boosts:
Exoskeletal Augmentation: Boosts Str by 10% = 250K + 100%, 20% = 500K + 300%, 30% = 1M + 500%.
Targeting Array: Boosts Dex as above.
Servo-Augmentation Unit: Boosts Agil as above.
Stealth fields increase or decrease your encounter rate. If set to 'Quiet', they lower your encounter rate by the percentage listed; if set to 'Noisy' they boost the encounter rate by twice the percentage listed. Typically, terrains have encounter rates between 5 and 45%, and stealth fields are rated between 20% and 80%. Stealth fields gradually use power while in use.
This device removes contaminants - particularly radiation - from the water, making it safe to drink. Notably, water purifiers are expensive, as is purified water. Buying a water collector and water purifier for your fortress means that you can make your own purified water, though.
You probably don't want to think too hard about where the 'processed meat' in each bar of 'Wasteland Jerky' is gathered from, but it keeps people alive. Of course, there are fresher and safer food sources, and if you have a Hydroponics Bay (or even just a Jerky Press), you can make your own 'delightful' foodstuffs to sell to errant travellers.