Hello and
to THP Aaron! Here you will find an amazing amount of info to help you with your growing and this place is full of friendly helpful people to assist with any questions you have when it comes to chiles.
Soil: There are so many types of soils you can use and so many things you can add. The soil and it's amendments are the most important component to growing. It holds the roots, nutrients, beneficial fungi and bacteria, water, etc. You can use the Walmart soil but if you are ever looking for a better soil some popular brands are pro mix bx, fafards, fox farm ocean forest. These might be a little expensive but are well worth it especially if you decide to expand into growing some of the superhot chiles. One of the most important things with soil in containers is drainage. Chiles hate wet feet and will not grow well if too wet. Try and find perlite and mix it into whatever soil you decide on at about a rate of 1/3. There are so many other things you can add to soil to make it better like slow release fertilizers, worm castings, compost, guano, lime, etc. You can find many many container soil mixes on this forum. Or you could just use the soil you have (preferably mixed with perlite if you can find it) as is and use liquid fertilizers to take care of nutrients.
Container: 5 gallon is your best bet if you have the room. Most times bigger is better, the more room the plant has to put out roots the bigger the plants will be. Also the plant will be slower to get root bound the larger the container. I use a mix of 5 gallon buckets, 10-15 gallon buckets and the blue reusable Walmart $1 shopping bags. Those work great and the plants don't get root bound.
Sun: Chiles should get at least 6 full hours of sunlight each day
Fertilizer: I use epsom salt as a foliar spray about every 2 weeks. About 1.5 tsp in a regular size spray bottle and mist the leaves early in the morning. I have never used sulfur powder myself so no idea on that. I don't know if your potting soil has fertilizer already in it but you need some type of fertilizer with N/P/K (nitrogen/phosphorus/potassium). All kinds you can use. Fish and kelp fertilizers are great, you could top dress with something like tomato tone or you could even use miracle gro if you can't find anything else. I used to use the miracle gro tomato when I first started growing as I heard it was better than the regular blue. Whatever ferts you use, you can follow label directions, use weekly at 1/2 the normal rate, or even use at every watering at around 1/4 of label directions. There are many many posts about the different fertilizers and members experiences with them on this forum.
Hope some of this is helpful to you and I hope your grow goes great (hope I didn't forget anything). Any other questions don't hesitate to ask