Gearing gives a simple ratio between torque and angular speed.
Say you have a motor which delivers torque T at 1000 rpm and a reduction ration of 10:1 then you will get an output at from the gearbox of 10T at 100rpm.
The key thing here is to estimate the torque required to rotate the drum, from what you have described, my educated guess would be that something in the couple of hundred watt range, typical of a small electric drill, should be fine once it is geared down to the relatively low speeds that you are talking about.
You can buy DC motors off the shelf with integrated fairly high reduction ratio gearboxes relatively cheaply which should give the sort of performance you are looking for.
I would also say that for this sort of application it is good to include a belt drive element in the transmission as this is a simple way to alter gear ratios if you need it and also has the advantage that it is simple and robust, being tolerant of minor misalignment and will tend to slip rather than break or stall the motor if something jams, which is also useful if you want to leave it unattended.
In terms of bearings pillow blocks are often the simplest solution for this sort of application as they are very simple to install, especially if you aren't very tight on space. and tend to be a good solution for low-volume and prototype production where you just want to support a shaft.
This also looks a lot like a barrel polisher these tend to work by having the drum sit on a pair of rollers with one or both rotating. This makes it very easy to remove the drum itself to put what you want to agitate in and get it out again, plus you can prepare one drum while the other is working as they aren't physically attached to the rotation mechanism.