When I started I purchased a full progression of King Ice Bears. In retrospect I wish I had purchased a stone at a time, of several different product ranges. Now I want to upgrade because the Kings don't do what I want of them, but I have no other frame of reference. For example, if I had bought a King 1k, a Shapton Pro 4K, an Arashiyama 6k, a Imanishi 10k, and maybe a Shapton Glass 220, then I would know a lot about the whole gambit of stones out there. As it is, I am replacing my Kings and the only thing I know is I don't want any more Kings. So buying one at a time, or several from a range of products, will not save you money, but you will learn more per dollar spent, and you will be a better informed sharpener than someone who did what I did and bought one line of stones. If you want to buy all at once, consider looking for a really well thought of coarse stone, the Latte for example, a highly though of 1k like a Nubatama, a mid grit like a 2k Naniwa SS, a popular fine stone like the Arashiyama 6k, then, especially if you are a straight razor honer, the Shapton Pro 15k. Add an Atoma 140 and you will have a single progression of stones, and know more about the stones that are out there than most on the forum. The only caveat is, like Adam said, a single line of stones may be great in one grit offering and abysmal in the next.
FWIW: The King Ice Bear is my favorite stone right now. It cuts reasonably quickly, has good feel, is more or less splash and go, has a pleasant mud, and leaves a good finish. My most expensive stone is a Naniwa SS 8k, and I find it has no feedback, so viscerally I don't feel like it does anything. My most frustrating stones are my 800 and 1200 Kings. Based on what other people say about their stones, it sounds like I have to work much longer, for a lesser edge on my Kings than most. Furthermore, I need to lap my Kings constantly. Since the 1k range is the workhorse of sharpening, I am beginning to rebuild my set there. Ken Schwartz has me set up with a Nubatama Ume 1k speckled extra hard. Part of why he suggested it was because it is among the harder stones out there and will contrast well with the softer Kings and Naniwa I currently have. So once I have spent time with the Nubatama I will be better able to solicit advice to hone in (pun intended) on what rings my bell in the mid and fine grit ranges.
Ultimately, most product out there is reasonably good. The difference lies more in preference and personal habit than objective quality. So anything you get will make your knives sharp, so have fun, be brave