To answer the first question: Yes, generally speaking all dies are interchangeable. If you've got a Dillon press (you don't) you may have to replace the locking ring. All of the die makers make a good product. Best bang for the buck is Lee, RCBS tends to be pricey but they are good products. Some like Lee because their tolerances tend to be a bit tighter than most. But, all of the die makers make good, serviceable products.
Now, as for what else you will need:
1. Lyman Reloading Manual. Read it, and read it again. Keep it on your bench. It will answer 99.9 percent of your questions and has good load data.
2. Scales. Beam or electronic, doesn't matter. Buy a good one, will last you a long time. Do not be tempted to buy one of the auto measuring scales. They work, but are slow.
3. Powder trickler. Let's you trickle powder to get your loads to the correct weight without going over and having to pull powder out of the pan. Will save you mondo time.
4. Case lube pad and lube. Don't get carried away with lube on cases. Too much screws up the clearances in your dies and will dent your cases. However, you need a little of it to keep you cases from getting stuck. Remember to wipe it off at the end.
5. Loading block. Plastic block to hold your shells while you reload them. I like to keep them upside down in the block until I am ready to put powder in them. The right side up ones have powder in them, the one with the funnel on it needs powder, and the upside down ones are emptys.
6. Powder funnel. Lets you pour powder into the shells.
7. Calipers. Good for measuring lengths and dimensions. Must have.
There are lots of other tools and goodies, but these are the basics. I would say that for now, don't get an auto powder measure. Spend some time measuring each load by hand to get the feel of what a correct measure of powder looks like for each load. Later on you can get an auto measure and speed things up. Before you even consider a progressive press, spend a lot of time with your single stage and understand the process and develop good safety habits. Those things have a lot going on and can bite you in the ass real hard if you don't have a good handle on the process.
Lastly but foremost, be safe. Wear safety glasses, primers especially are volatile. Be methodical and develop habits that are consistent and safe. Good habits can save you from making a critical brain fade error. You are talking multiple cartridge types, keep your constituents organized, double check them when you load, store them separately and only have what you are loading on your bench. Inspect your cases for damage, throw out any that are split, dented or suspect. When using load data, do not start at max loads, start at the lower and work your way up. Generally, the most accurate load for any firearm will be between min and max somewhere. If you don't know, don't guess; ask a question, we all love to help out. Never, never, never, exceed the max published load or mix powders.
Lastly, load lots, shoot often. There is a great deal of satisfaction in seeing how your shooting improves when developing accurate loads for your firearms.