There is a lot of information on Taiwan on the net but , rashy and vest would be OK November is when the Alaskan storm swell begin to grow and NE swell begin to prowl down the east coast from Taitung ( Taidong ) depending on we spell it are some great breaks. No basic beginner stuff as there is some power building. Be aware too that swimming and lifeguards are not common so you have to be self sufficient in looking after yourself.
There is Bashien Dong a spot I like , and others at various river mouths.
Note too that if a Typhoon is building the coast guard may call all surfers in. You will need to comply.
Hiring boards is mostly at populated beaches which look like this
Don't mess with the umbrella hire lady!!!!
some of the local hire shops have a select range of very pre-loved boards
there are a lot of foamies available like the blue and white striped one.
Typhoon but small surf near Taitung looks like this
However your trip should be good if you just follow the rules
Try Surf Taiwan as a look up site,they give you a seasonal breakdown and a few thoughts on spots.