Before you worry about which tools learn how to sharpen tools to a razors sharpness without removing too much steel. If they can shave the hair off your arm with no tugging they will cut quicker, better and safer.
My basic list would include a Miller Falls 106 6 piece carving set or its equivalent. Ebay $25.00 I use three or maybe four of these at most. Small gouge, veneer, two of the skews.
Three flat bottom, bent dog leg skew chisels, one left, one right and one straight cut. EBay, Ramelson maker about 15.00 each
1/4", 1/2" wood chisels,
Draw knife. Cabinet makers half round and flat files. Round file and a few rifler files as well.
Pfeil 15/16 or 5/8 skew chisel, 7/14 shallow gouge, 1/2" bent flat straight chisel and gouge if you don't have the Miller Falls set. Veneer also.
pfeil Swiss made Undercutting Tools left, right and straight, same as full size set but sometimes comes in handy but in tight spots. They are just a smaller version of the dog leg chisels. $45.00
Number 6 and 10 chip carving knives.
Burnisher (Tringular) to compress wood fibers if you come across a soft area. It helps by compressing the wood so it cuts cleaner. I use it a lot on stocks with hidden and not so hidden burls. Burl can be very hard but the wood around it can be soft or even the reverse. Burls should be in the butt area not the grip but they do not listen to me.
Ca thin glue to help strengthen weak areas or soft areas. Not to be used where it shows as it can make finishing difficult.
Diamond whet stones (3) to touch up an edge quickly. Woodcraft DMT Mini Hone, Set of 3 $22.99
Leather strop.
Dead Blow Hammer.
Bessey Parallel Bar Clamp 24" F clamp will do as well.
Tormek sharpening system for proper resharpen when needed.
I listed 14-17 total chisels but doubt half of them get used much on most jobs.
Full disclaimer I have my own Gemni duplicator machine for my own use and don't duplicate all balks to the same level of in-letting. I find that dense, hard stocks are best almost completely inlet, to the maximum of my machines and my ability, which is 96-97%, while normal or softer stock blanks are duplicated to about 90-95% and fit up just as fast from there. The difference sounds small but it is not. A 90% inlet hard blank might as well not be inlet at all. Normal or soft stocks almost are like carving soap with razor sharp tools. Hard stocks are just that, harder to carve but they give you the best inlet job. For your pride and joy use hard, dense wood for a klunker user softer stuff.
The quality of the blank makes all the difference. I like hard, dense English or a nice Crotch Black Walnut as a rule. Hate Maple of all sorts. Circassian, Claro and Bastonge work well most of the time, depending on the blank. But I had a dense Bastonge walnut, with extreme curl in it that took ten times the normal working time to inlet from a 97% blank. It was like carving a wash board. Razor sharp tools only would cut it. Black Walnut inlets quickly, English and French cleanly, better than Black, but longer for me and Claro is in between depending on density and burl or curl grain.
If you make one mistake you might, might recover but after two you are nearing the wood pile fast. And if I had to make a living doing this I look like a Sudanese on a hunger strike. I admire anyone who can do this for a living. To do it well is very hard.
