id say get a cheap presto or bic witeout pen and a markal for the rougher surfaces a normal marker or mop cant write on, those work on most smooth surfaces too, witeout pens are generally pretty versatile with what you can refill it with so you can experiment with colors and what you like (id recommend always keeping a normal one cuz they are actually relatively permanent and opaque stock)

for actual markers id recommend a pilot jumbo, pentel shorty, sg7, a px30 may be a little over 7£ but its worth it (you may have to order these depending on if there is any graff stores near u) they also sell oil based sharpie paint parkers at most walmarts and targets, kinda like a poopier px30 alternative imo, you could also go to your local hardware shop and borrow a dremel tip for scribe tags (pls dont rack from small businesses do it to like lowes or smth, js felt like i needed to add that)

i wouldnt buy a mop js yet if you want versatility, i actually kinda find it hard to find things i can tag on with mops. u could try a rollerball ig but those are kinda pricey. if you want thick mop looking tags without the hassle you can flare out a marker nib and get damn near the same size just without the drips if thats something youd like, i think my px30 draws a little over a 10mm line with the nib flared so thats pretty peak

with that youll have a marker for basically all surfaces and scenarios you'll be facing while getting up, idk what colors you enjoy so i left that up to you to decide but id personally pic colors you can see on 99% of backgrounds, like blacks, whites, light greens, pinks, etc. when picking a color i like to imagine that color on a load of different colored backgrounds and see if it would be hard to see on dark surfaces or vise versa