To help keep it cool, in summer have plants that cast a lot of shade. Water lillies, duckweed, etc. You can also just toss a frozen waterbottle or two in there to beat the heat. You'll have to change the bottles when they melt so it can be a hassle but still effective. If you are doing water changes, you can also use this time to add slightly cooler water back in, but don't get it too cold or you'll shock your fish. Another option is to have a fan pointing at the surface of the water; this will cause evaporation and cool the tub, but you will need to replace the water more often.
The best fish depends on the type of tub. Goldfish tubs are pretty common, but they need a bigger tub. If you've only got a smaller one then guppies are an excellent choice. They are flashy enough to keep you interested, playfull, and they'll eat just about anything. If it's going to be a long-term tub you can also save money by getting just a trio, two females and one male and they'll populate the whole thing for you; though an all-male tub would be stunning. Mosquitofish are another good choice; I haven't researched it but I believe you can put mosquitofish and guppies together.
I personally would do no substrate and if you have to have underwater plants put them in pots on top of a raised plastic lightgrate. You want to find one that your fish can't fit through the holes. If you're using smaller fish like mosquitofish/guppies this may be difficult. You can purchase plastic canvas at almost any craft store that will do the job for smaller fish, but you'll probably need to attach multiple pieces together as they don't come bigger than 1'x 2.5' (At least that I've seen) I reccommend putting in a drainage hole near the bottom of one side under where the grate is in case you need to do water changes. Obviously you want to use a valve that can be opened and closed. It will pull from the water under the grate first, which gets out the dirty water (presumably why you need a change) first. Not a requirement, especially if you don't plan on water changes but I like to have it as a 'just in case'.
What are your temperatures in winter? You may need to bring your tub inside or purchase a small heater. Also, does it rain a lot where you are? If so you'll want to put in an overflow (A hole near the top, no valve required unless you need a hose to carry the water away from your tub.) It would be a good idea to cover the inside of your overflow with cheesecloth or similar so fish don't fall out as the water level rises.
There are two types of tubs that I have seen, and which you go with is really a matter of personal preference. There are plastic tubs that you buy (I used a 50 gallon rainbarrel because it had a built-in overflow and drainage system.) Or a wooden tub that you make, with pond liner inside. Both are good options. The wooden ones seem to be shallower with more surface area, and the plastic ones that I've seen are usually deeper with less surface area, assuming the same gallons for both. It's mostly an aesthetics thing, whatever you think looks good.
If your winter is cold and you choose to bring in your tub, I would put wheels on the bottom of a wooden tub to make transport easier. Make sure you get locking wheels so they won't move around when you don't want them to though. Or place your plasic tub on something with wheels, I used five rolling plant stands superglued to the bottom. One in each corner and one in the middle, but depending on the tub size you could do just 4. I've also seen a flat wooden frame built from 2x4s with carpet on top to keep the tub from slipping and wheels on the bottom.
Sorry, I know this was long-winded but I hope it helps. Depending on your area you may need to be wary of raccoons or herons as well, something to keep in mind.