Start by estimating the accuracy of your temperature sensor and controller. You're going to need to do some comparisons with reliable thermometers for this step. I'm guessing you don't have any laboratory grade thermometers at home that have recently been professionally calibrated. (Who does, really?)
Start by finding two or three digital cooking thermometers (preferably different models) that seem trustworthy. Then calibrate your PID controller by measuring the temperature of a mixture of equal parts crushed ice and water. It should be 0 °C. While you're at it, use the ice slush to check the accuracy of the cooking thermometers you found. Recalibrate or replace them as needed. Finally, heat some water to around 60 °C (or whatever temperature your think you'll be using most often for cooking). Then measure the temperature with your PID controller and the cooking thermometers. That should give you a pretty good idea of how accurate your PID controller will be during cooking. (If you find that your PID controller is accurate at ice temperatures, but quite a bit off at higher temperatures, you likely need a new temperature sensor.)
Sous vide accuracy is frequently in the neighborhood of +/- 0.1 °C, but +/- 0.5 °C is often good enough. I'm not sure what "low accuracy" means, but let's say, for example, that you estimate your accuracy to be +/- 2.0 °C. In that case, simply raise the temperature setting by 2 °C to compensate for the margin of error. It might result in a different level of doneness than you want, but the food will probably be safe.
Take a look at Douglas Baldwin's A Practical Guide to Sous Vide Cooking. Not only does it have some excellent recipes for beginners, but it also has some great safety information. If the food is to be consumed by pregnant women, you don't just want it to be cooked. You want it pasteurized. The guide includes tables for looking up the pasteurization time for fish, poultry, and meat (beef, pork, and lamb). If the meat is starting frozen, add about 30 minutes to the cooking time. If a recipe's going to take too long, use the tables to adjust the meat thickness or temperature in order to reduce the cooking time to your preference. Keep in mind that your shouldn't start the timer until the food is in the water bath and the water is up to temperature. So, save time by heating the water first thing when you're ready to cook.
Since temperature control is so vital to sous vide cooking, the circulation serves to make sure that all of the water is moving and of an even temperature. If you just had a heating element submerged without a circulator, you would get some convection currents, but there would be hot and cold spots in your water bath. If these differences were even just a few degrees, you could end up with proteins not hitting their coagulation temperatures, connective tissues not softening, pectin not broken down, etc. All in all, it would defeat the purpose of this cooking method!
As for the differentiation between "circulators" and "water ovens", there may not be one. Frequently the actual thermal unit and pump is referred to as the "circulator" and the whole assembly with a vessel and water is referred to as the "oven", but I'd check the specs of each model to see whether it has all the parts you're looking for.
Best Answer
Coolers (chilly bins) are ideal sous-vide cooking vessels as they are well insulated, and thus conserve energy and avoid temperature varying across the water bath.
Most sous-vide cooking happens at less than 80°C (176°F), so the plastic will stand up fine.
Many commercial clip on sous-vide cookers are only suitable for fish tank style containers (thin walled). These tanks look pretty, but waste a lot of energy, and can struggle to keep the same temperature throughout all the water. An interchangeable clip, or wide reach clip is more useful for coolers or other insulated vessels.
Specifically with the Chefsteps Joule sous-vide cooker: it seems to have a powerful magnet in its foot, so if you place a sheet of coated steel on the bottom of your cooler, you won't even need a clip.