As a start: I did some 10-12 years in IT before shifting over to law enforcement. When I did IT it was as a IT-technician and later as a SystemTech/Admin in the healthcare field working mainly with radiology (X-ray) systems.
My thoughts and ideas in this post is based around my experience from above employments, and even if those jobs included working with 4500+ clients, centralized software distribution / desktop management I think some of might be applicable to smaller IT-enviroments. Also, they are based on the angle of you using tools in your professional career. Shortly mentioning my private USB-setup at the end of the post.
As english is not my primary language - and I'm a fast typer - I ask that you please excuse any errors in grammar and/or spelling
Have one drive with many partitions, with many software programs, or a few different USB drives with different purposes (like some bootable - I believe you can have a bootable partition with non-bootable partitions on a single drive, but I don't know for sure, or the pros/cons)?
Type (e.g. SSD or non-SSD) and size of drive(s)? Other considerations for the drive(s)
I've used a SSD-drive with a home made boot-prompt that allowed you to choose which image to apply to a computer, for easy resetting should anything happen to a client that needs to get back up into production asap. I'm quite sure you could add - for example - a lightweight linux-distro of some kind to a bootable partition and use that to perform changes on clients, should you need to. You could also use a USB-stick with a bootable LIVE-distro of some kind of linux on.
We acctually used more USB-sticks with different tools on and such than we did single drives. The reason for this being that it was easier for us to keep the separate tools updated and if one needed tool X and another tool Z they didn't have to pass the SSD around.
The only problem I see with using USB-sticks instead of actual harddrives are that some older computers can't USB-boot. On the other hand I vaguely remember Windows 7 seriously disliking being booted from external USB-harddrives, if it was even possible back when I was at it.
You could absolutely have a bootable partition and then some other partitions with tools for example Windows and what not on them. Should be no problem. Choose USB-boot in the BIOS or Firmware if you want to boot from the disc at startup, if not, the other partitions with the tools will be visible in the computers own OS when you've started the original OS, provided the operating system supports the format of the disc (FAT, HFS and what not). Actually this sounds like a pretty decent solution for you.
...also, don't forget about the awesome Hiren's Boot CD which can be downloaded for free. It's a good tool for diagnosing computers as long as they have a CD/DVD-reader (or potentially can boot from USB if you want to fiddle with applying the .iso to a USB-stick). Hiren's also contains tools for lost Windows-passwords and whatnot
What software utilities do you recommend based on your experiences and why?
For hardware diagnostics there are often tools provided by the company that builds the computers, at least if it is Windows-based machines. I know DELL and such have service-partitions that you can boot on to and use to diagnose your computer. The problem I have with these "provided" tools are that I've used them many times and gotten no errors reported back to me, but when I later check for example what I suspect to be faulty RAM-modules with another tool, say MemTest or something, I get loads of errors. So I wouldn't trust them to babysit one of my kidneys, should it spontaneously fall out.
The project Portable Apps is a software suite built to be run from a single USB-stick worth checking out. Although not bootable it contains tools for many different kind of things and also things like OpenOffice, and it's completely free. One problem with this is if your employer or system administrator has disabled using EXE-files not vetted by a central management (like an Active Directory, Novell or something), but if you - like I did - work for the IT-department then it should be possible to use "Run as Administrator" to get it to start.
There are of course tools for mostly everything. For network / TCP-based monitoring and diagnostics I'd suggest using WireShark which is an excellent tool to analyze TCP and UDP trafic.
If you are in need of tools for something more specific please ask and maybe I can give you a hint.
Anything else your experience has taught you...
Keep a spare copy / backup of your toolbox. Ie. an image of the disc or sticks that you use. It doesn't have to be a spare identical physical disc (costs and so on). I once worked on a computer with a drive that had faulty sectors on it or something and in the process of reformatting the drive accidently formatted my own "tool-drive". Felt like an idiot and a couple of hours added to the whole mess was the result of that, and an important lession learned.
I prefered to keep the disc / sticks together with tools (screwdrivers of all kinds, plyers, flashlight, tweezers, a can of compressed air and what not) neatly organized in a pouch or small bag. The EDC-freak in me kept it neat and tidy and that way you also know that you have both the soft(ware) and the hard(ware) tools that you need should you find yourself in a situation where you need to remove a case, a disc, straighten out the pins in a DVI-connector or what ever.
Also, you can never have ethernet-cables that are too long (or well... you CAN but you get my point).
On a more personal level
At the moment I do not carry a USB-stick but that's mainly due to my old one breaking. I have a USB-stick at another location than home with insurance information, copies / pictures of prized posessions with their serial / IMEI-numbers and stuff and also copies of mine and loves ones passports / ID-cards and insurance and healthcare info for my pets.
Wow, that was a lot of text. Hope it helps somewhat.