What's a typical rate of climb for a hot air balloon, assuming stable air with no updrafts? I'm thinking of the classic 'sightseeing ride' type of balloon here.
It very much depends on the balloon, but 2 metres/second in actual flight is pretty typical, while most are capable of something like 3-5 m/s ascent/descent if required. Ascent and descent speeds are normally about the same for a particular balloon, but this isn't a hard and fast rule
"sport" balloons being are capable of moderately less comfortable ascent/descent speeds in the range of 5 to 10 m/s
The good balloonist will try to limit the vertical speed to 2 - 3 m/s (400-600 ft/minute) to make it easier for the passengers to accommodate to the pressure change and avoid ear barotrauma. This is the main factor; technically the balloon is capable of higher vertical speeds.
Much depends on the temperature profile of the atmosphere over altitude. The gas in the balloon will expand adiabatically, and the density difference to the surrounding air will change if the surrounding air doesn't cool at the same rate. For dry air, this cooling rate is 6.5°C per 1000m. If the atmosphere has a higher cooling rate, the balloon will accelerate, if the rate is lower, climb speed will bleed off the higher the balloon climbs.
For that reason, you will rarely see balloons flying at the same time as gliders. Gliders need thermals, which are best in air with a high cooling rate, whereas thermals will make the job of limiting vertical speeds in a balloon much harder.
Blimps need to keep their hull pressurized, and here the descent rate is limited by the ability to pump air into the ballonets.