Very good questions, and you will get about 20 answers to each one :-D It is up to you to pick the right answer for you.
I'm very cheap, so have constructed most of my own stuff. There is always a balance between cost and objectives, but if cost is primary and you don't have the time to make your own boxes/frames, the basics I'd recommend to start....
2 deeps for brood, 2 mediums, all one-peice plastic frames for them(cheaper than foundation and frames seperately, I think). Inner cover, outer cover, cheap bottom board. Veil, smoker, hive tool. you can use your own gloves or pay $7 for some canvas gloves. Wear a light colored spring jacket and jeans (unless you don't want to use a jacket/gloves). To me that would be the cheapest basics. The plastic frames/foundation you can scrape and drain when harvesting honey and re-use.
And make sure that you know a fellow beekeeper who can provide some assistance/brood/split if you run into trouble. Get frosting buckets from the bakery for harvest time and a couple cheap paint strainers to keep the wax out.
If you don't mind spending a little more, I like wood frames with plastic foundation, go with all mediums, a screened bottom board, a few more supers, at least 2 hives, an extractor, italian hive tool, specialized feeders, queen excluders, etc. Then you can get into the small cell foundation, foundationless, etc.
I didn't buy a starter kit, but purchased a 2 deep hive from another beekeeper. He also sold me a small old smoker and some misc. hive equipment that I don't use anymore. You'd have to do the math to see if they are worth it since they ususally come with only one deep super.