Don’t know if you want to go crazy but a starting clamp and maybe a cheap set of tennis polyester might be good to have. You can go cheap with a starting clamp, but just to let you know, you get what you pay for. A 30usd clamp might slip but a 200+usd Yonex starting clamp will amaze you and so far for me has lasted a long time 13 years so far. I use it as an extender when I cut short from a reel which is all the time, because my tension head is a little more further away then normal machines. When I measure now for my mains I am using 7 racket lengths for my mains and 6 minus about half the grip for my crosses, maybe gives me about 3.5 inches to tie my knots. I usually get about 23.5 rackets from a reel. BG 66 Ultimax in Japan now on Mercari Japan runs about ¥900 a set and a reel 200m is about ¥13500, that comes out to less than ¥600 a set you do the math.
As I live in Japan now I have learned to become a frugal stringer looking for cheaper tools. From Aliexpress I have found a few useful tools a grommet grinder and a grommet remover tool. The grinder can help you turn grommets or push them out. I usually try to push them out when I inspect the racket, but sometimes I might miss a grommet that I thought might be ok but when I put the string in looks bad, so the grommet remover tool which looks like a screw on the end is helpful to me to pull it out instead of push where the grommet grinder has trouble pushing while I have mains installed.
My last goto tool is like a 30° short bent nose plier. I found at my local hardeware store for less than ¥400 which I use at home, but you can be a dumb ass like me and spend ¥1800 for a Japanese Fujiya brand bent nose plier MP9AT-110, a 3 Peaks cutter CN-130 ¥4700 which can cut piano wire, ¥6500 for tools at your hardware shop can probably find for less than ¥1000 and do the same thing, overkill but hey, puts a smile on my face =)
I personally use a floating clamp on my crosses, I use it to do finishing knots on my crosses instead of a starting knot and a finishing knot, most people will anchor their cross, a flying clamp helps me tension strings without anchoring the cross, then after a few crosses tensioned I can go back and tension my first cross and then tie off, this puts less tension on my knot if I were to anchor and then pull.
Grommets, yea my goto are 2.1 and 2.7, I usually shove the 2.7 in but sometimes I bend them and need to use a 2.6, but if you can shove a 2.7 in you don’t have to worry about it slipping out. The U shaped grommets at 1-2 and 3-4 I usually have and a L shaped 2.6 in case the frame shows some wear from stringing I would use those. I store in a small fishing tackle box.
Alcohol, q-tips, a wire brush might come in handy for your clamps. A good movie too while you clean them.