Chlorine works fine in a hot tub. It is a bit more temperature and pH sensitive than bromine but is easy and the least expensive.
There is a lot of misinformation about bromine. Bromine tablets in a floater are NOT enough. First, sodium bromide has to be added to the water to create a bromine bank that the oxidizer (chlorine, MPS, or ozone) converts into hypobromous acid. Bromine tablets do contain either chlorine or MPS but they dissolve very slowly and it can take a long time to get enough bromine reserve in the water for them to work properly if you don't add the sodium bromide first. IMHO, the best shock for a bromine spa is bleach.

I have used both in a portable spa. They both have their own unique sets of problems. For example, I found that pH control was much harder with bromine. pH was always dropping.