Welcome to the tool collection part of life. From now on you collect knowledge, skills, and implements to do the things that you want to do. While you're building your Amazon list, add one of these screwdrivers. They're $15 so maybe order 3 so that you have one in the car, one in the kitchen junk drawer and one in your office. They are very high quality, cover probably 90% of the fasteners that you'll encounter around the house (furniture, cabinets, TV mounts, outlets, drawer pulls, washer dryer pipe clamps, packaging, bicycle brakes, etc.), and should last a lifetime.
I've posted in a couple other comments in this thread, but all together:
Dewalt Gyroscopic Screwdriver. Not really necessary if you do one or two laptops a day, but very nice to have when you starting doing 10+ per day.
Klein Scout Pro 3 Network Tester
I've also gotten plenty of use out of the Klein Tools Electronics Screwdriver and Regular Screwdriver sets.
I'm sure any kind of cat6 cable cutter is fine, but I happen to like this one.
For non-standard tools:
For anything besides a cat5/6 sheath, or to cut zip-ties, I have used these wire strippers for many years - still sharp.
When you just need to chop something in half: Knipex Cutters. I've also found them quite useful for modifying Chromebook cases that aren't meant of the model they've been put on.
Optical Power Meter, also an RJ-45 coupler and a long patch cord, that way you can go and sit in comfort somewhere while consoled up to switch. Others have mentioned this too but also a good VFL (visual fault locator) if you work with fiber. Make your company pay for these things unless you’re like me and want to take tools with you to the next job, and you do work on the side.
Edit: Adding Snips! Learn how to hold and use them.
Klein Tools 21010-6-SEN Free Fall Snip, Carbon Steel https://www.amazon.com/dp/B00HAN2RRY/ref=cm_sw_r_cp_api_glt_fabc_SY2N7FM7W3FV5VXD32V3?_encoding=UTF8&psc=1
Fluke Networks MT-8200-60-KIT IntelliTone Pro 200 Toner and Probe Kit, IntelliTone Probe and Toner Kit https://www.amazon.com/dp/B00N2S6RPY/ref=cm_sw_r_cp_api_glt_fabc_BD400BK8ZZEQ8NQXGCST
Also Klein makes great tools I carry the following screw drivers: 11-1, a flat head, and a micro 4-1 (all non ratcheting)
Klein Tools 32500 Multi-Bit Screwdriver / Nut Driver 11-in-1 Multi Tool, 8 Industrial Strength Bits, 3 Nut Driver Sizes, Cushion Grip Handle https://www.amazon.com/dp/B0015SBILG/ref=cm_sw_r_cp_api_glt_fabc_C8JX8H7RSA1RAPZ2X0H7
Precision Screwdriver Set, 4-in-1 Electronics Screwdriver with Industrial Strength Phillips and Slotted Bits https://www.amazon.com/dp/B01EOY7LTA/ref=cm_sw_r_cp_api_glt_fabc_TXPYFR74Q7CKJDJTJJGJ
Fluke Networks MT-8200-60-KIT IntelliTone Pro 200 Toner and Probe Kit, IntelliTone Probe and Toner Kit https://www.amazon.com/dp/B00N2S6RPY/ref=cm_sw_r_cp_api_glt_fabc_BD400BK8ZZEQ8NQXGCST