Yes, they will get the job done, all the steels you mentioned can be sharpened. What Norton stones were you considering? They make a few different ones:
Crystolon (silicon carbide, approx. 150 to 400 Japanese grit range); cut fairly quick (but slower than waterstones and diamond) and wear fairly quickly, but not compared to waterstones, don’t come in what I would consider a finishing grit.
India (Aluminum Oxide, 220 to 500 grit); come in some finer grits, OK for finishing on a working edge, don’t cut quite as quick as Crystolon but wear very slowly (are fairly hard, I believe this is why they finish better than the Crystolon of comparable grit)
Arkansas; the soft I don’t use. The ultra fine / translucent (Natural 1,200 to 2,000 Grit) are the finest and most consistent Arkansas stones I’ve come across. They cut fairly slowly, don’t wear at all, and can put a hair popping edge on a knife.
Norton waterstones (220 – 8,000 Grit); I don’t have personal experience with these but I’ve heard good things. I went with a less expensive waterstone set. waterstones are faster and have a larger grit range than the above stones, if you don’t mind making a mess.
Diamond? I have worn out quite a few quality diamond (DMT and EZE-Lap) hones but I do press hard, they are expensive, and cut fast but I dont like them for finishing (although I havent tried the new DMT 8000 grit). Other types / systems you might consider? Ceramic (Spyderco and others, 1000 – 4000 grit), Waterstones (many brands, 80 – 30,000 grit) scary sharp (Micro finishing film, PSA backed and non, 100 – 30,000 grit) spyderco sharpmaker, Lansky, and Edge-Pro systems. There are lots of options out there, search around the forums and you’ll find as huge a variety as there are opinions about witch are best.