The bum pain gets less the more you cycle, but padded shorts are essential (unless you are doing very short rides) in my opinion.
Roadie fashion is all about the Lycra, but mountain bikers wear baggier shorts over the top, so go for that look if you prefer it.
Agree you should learn how to fix a puncture & carry spare inner tube, tyre levers, pump. Or have another strategy to get home! In fact it’s always best to have a strategy in case of mechanical failure, snapped chain which is rare but can happen.
Wear high viz - seriously the amount of cyclists I see wearing black / grey on a dark dull evening is amazing. I only buy cycling kit in ridiculous colours as I like to be seen. Also lights can help you be seen, even in daylight.
The wobbling comes with practice. Just keep going.
If you are off roading, please remember horses can be scared of bikes so if approaching from behind please call out (in a non-sudden manner) and check if safe to pass. I ride horses too and know from experience bikes trying to whizz/squeeze past is an accident in the making.
Join Strava and get involved in some friendly competition, even if just with yourself. Love getting PBs and seeing my improvement