I'd avoid the stamped knives typically found in big box stores or any set for that matter. Shun's are fine if you have an affinity for Suminagashi clad blades but the geometry and handles are miserable for a working knife. If you scratch that faux Damascus it's permanent. Globals are a RPITA to sharpen properly but they were the first widely available J-knives in the US. I sold mine off several years ago and never looked back. They served me well but for the money there are a LOT of better choices today.
There is no one "best" brand but the suggestion for Tojiro DP was very solid. They are great working knives at a reasonable price point. Watch Korin for 15% off sales that they have twice a year. I've bought from Mark at CKTG as well. He is also a good source for stones.
Budget and sharpening skill should be considered as well as if the OP wants a Western edge or single bevel J-knives. Then there is the question of carbon Vs SS.
Today I prefer WA variants that offer a Western edge and traditional Japanese handles. Masamoto KS series is an excellent choice that offers this styling but they are well into the mid-price range unlike the Tojiros at the lower end of the price spectrum for a quality knife.
I'd highly recommend the JCK (Kagayaki) original series. I have one of the WA Gyutos and aside from the handle, Kanji and mirror finish it stands up very well to the Suisin Honyaki which is several times more expensive. I'll leave a link.
I'd suggest starting with the following;
A 240-270MM Gyuto based on size preference. I use 240 the most at home but in a professional kitchen 270 is the norm.
A petty in the 120mm range.
Those two knives alone will take you a very long ways. You do not need to buy a set or even the same brand. From there I'd expand to a sujihiki or slicer of choice, a chinese cleaver and a bread knife. Mac probably has the best value going in a bread knife.
http://japanesechefsknife.com/KAGAYAKIVG-10.html