Wouldn't call myself an expert, but we do some tin plating at the place where I work.
So for what it's worth, here's what I know. Remember though, this relates to medium-scale industrial process (we plate up to 3m long and 1 tonne mass). How relevant it will be to you if you're using a table top setup I don't know.
Potassium Stannate is the usually the electrolyte of choice. We use an "Alkali Tin" process, because of compatibility issues with other processes. It's rather an old fashioned way, and most platers prefer the "Acid Tin" these days, particularly for non-ferrous jobs.
What's the purpose of the plating? Are you after specified coating thickness, specific Ra figure, or degree of corrosion protection?
If you are just after an "eyeball-good" finish, then tin is a pretty forgiving and straightforward stuff to plate. It throws well into hollow sections, and doesn't build up on outside corners too badly, providing you keep plating times sensible.
Current density will vary depending on the type and shape of the work, size of tank, proximity to the electrodes, etc. There are an awful lot of variables, but if you have ever plated nickle, then the process parameters are not too different, so that would be a good place to start.
The main difference from nickle is that we use plain steel anodes and salt replenishment, rather than sacrificial anodes. Again this may more relevant to industrial practice where we are plating to specification. We have a process chemist who monitors the remaining metal content in the solution, and calculates how much salt to add.
If you are just plating for an attractive finish, then provided you keep the temperature and current density constant between jobs, when the plating time starts to get long, you know the solution is getting tired.
We keep the working solutions at 55C, but as with anything in industry it's a trade off between process cost and productivity. Higher temperature gives shorter plating times, but heating tanks that size is expensive. Running the solution too warm can cause poor finish and high reject rates. Too cold and plating times get very long and can result in poor adhesion.
We used to use constant air agitation, but to be honest, the bubblers broke down a long time ago. We never bothered repairing them and it seemed to make no difference to the finish.
Potassium Stannate itself isn't that harmful. Don't swallow any, get it in your eyes or inhale it. Take sensible precautions.
The main hazard with it will be the acid (or caustic) you have to use to pull the solution pH. If you are already doing plating work, you will be familiar with the precautions, I hope.