One thing to remember another coat will not fix a high place or ridge. Either scrap or sand these off before next coat. And on knife size I would split the difference on the 3 and 5" and get a 4" they have them at Lowe's in the cobalt brand. It has become my work horse, I use it to get mud out of the bucket, to run my corners, and to put a thin coat on your final where it leaves that hump where the mud meets the board. It is stiff enough for about anything you want it to do. This little 4" knife has cut down on a lot of my sanding. In fact it is about the only knife I use now. I also hate knifes and the bread pan, I use a hawk and trowels. But for DIY I think knifes would be better.
I know this is a couple of weeks old, but I think beginners should understand the importance of using water. Keep a bucket around so you can wet your tools here and there. Beginners will inevitably overwork the mud and once it starts drying even a little it will leave marks and be a disaster. If the knife is wet it will smooth out the compound nicely as it rewets it. Also, add water if using premix to get a consistency you like working with.