99% of dies use standard 7/8-14 thread (7/8" major diameter, 14 threads per inch, also known as 7/8 NF or National Fine as it's a standardized thread) so are completely interchangeable. Even the shell holders that snap onto the ram are usually interchangeable between brands. The only dies I've heard of that aren't interchangeable are the large format dies for things like some of the larger elephant cartridges and .50BMG and some odd ball Dillon dies from decades past that they used a non-standard thread for some reason or another.
You can get a Lee press, or an RCBS, or a Dillon, or ... you get the idea.
I'm currently using an RCBS Partner Press. It's their smallest one which suits me fine as I have it bolted to some 2x4's and clamp it to a desk when I want to reload. I live in an apartment so it's best for my situation.
Most brands sell starter sets that include almost everything you need. They are usually just lacking a case trimmer and of course dies. Sometimes you save almost nothing over buying the components individually, sometimes you save a lot, you'll have to check by adding up the individual components.
Any of the US brands have very good to downright amazing customer service so it's hard to go wrong even with the low end stuff (usually considered to be Lee).
Redding makes very good products and their T7 turret press is excellent. Personally to get started I'd just get a single stage as they're usually quite a bit less expensive and if you are doing low production like you describe you don't really need a turret or progressive press.
I'd pick up a reloading manual or two and read the front sections at least once or twice. They usually cover a basic introduction to reloading.
Another book I found useful when I was getting started as "The ABC's of Reloading". It doesn't have any load data but is an excellent introduction to reloading.
Going through my reloading process in my head I use the following items (not brand specific):
-tumbler to clean the brass (dry media, stainless pins, or ultrasonic; all have their pros and cons)
-press
-die set (full length sizing, neck sizing, bullet seating and crimping, Lee factory crimp die)
-case trimmer
-deburring tool (trimming leaves burs in and out of the case mouth)
-hand primer (most presses have a priming tool built in but a hand primer is faster)
-an accurate scale (cheap digital scales have huge tolerances on them and can't be trusted; go balance beam or premium digital)
-caliper (measures things down to .001")
