Press: Rockchucker converted to Lock-n-load, for home use, Harrell's for range use.
Dies: For factory chambers, you might try the combination of Lee Collet, and Redding body dies, and Forster Ultra seater
.
Trimmer: Wilson (Keep your Wilson stuff lightly oiled between uses. They they are the standard, but rust easily.)
Scale: any of the RCBS balance scales that have agate under the knife edges, then have it tuned up or do it yourself, if you are handy
Powder Measure: any that have some sort of system so that they can be accurately returned to the same setting. I have a Harrell's that I like.
Priming tool: I have several hand tools. They all work, but I have a 21st Century that I think that I am going to like better than my Sinclair. It is Stainless, and does not have a magazine. I prefer "single shot" hand priming tools. I seat by feel, as do almost all short range benchrest shooters.
Lube: RCBS Case Lube II (water soluble) applied lightly and evenly with fingers, wiped off with a wet cloth.
Case neck powder fouling removal: Outside 0000 steel wool : Inside: an old bronze bore brush on an accessory handle, pushed in and out about 3 times. Don't clean down to the brass on the inside. Leave a film.
Primer pockets: For flash hole burrs use a tool that is appropriate to the flash hole size. I don't cut the bottoms of pockets. I think that a cutter adjusted to just clean the deepest pocket is good for powder fouling, but doing this every time does not yield better accuracy.
Manual: Look several over and buy the one that you like best. I like the Nosler, but I also have Hornady, Sierra, Hodgdon, Lee, and Speer that I have picked up over the years. These days, with the internet, I think that they are less needed for data, but they all have instructions for the beginner that are good to read, more than once.
I prefer dial calipers to digital, because they are just as easy for me to read, more economical (don't spend a lot of money for reloading.) and you won't get caught with a dead battery.
If you want to play with turning necks, just make sure that the tool has a carbide mandrel. They have less tendency to transfer brass from the case. A 1" micrometer that reads to .0001 and a neck micrometer are good if you are turning necks. For the latter I like my Holland. Both are technique sensitive, so practice if you get them.
Loading Blocks: I have some old MTM universal that serve a variety of calibers, as well as wood and plastic that are head size specific. They all work.
Concentricity gauge: Sinclair
Bump Gauge (attachment for calipers): Hornady (formerly Stoney Point)
Loaded round length measured off of bullet ogive gauge: Hornady
Seating depth tool: Sinclair, and or Hornady
Now, on the loading at the range thing....
I have done both, and for me trying to work up loads by doing test rounds at home is like running with one shoe on, pointless and inefficient. You will wast a lot of time, components, barrel steel, fuel, and never get to as sharp of a tune. It does have one "good" feature. You will not be guilty of being different. Of course every short rang benchrest shooter that I have ever met or talked to works up his loads at the range, but you copy who you want to shoot like.
Another thing, get something to look at the wind. If you have not seen a row of flags that are posted between a shooter and the target, you may not know how much difference there is between what you feel at the bench, and what is going on at various yardages down range. I just love it when fellows tell me that they only test loads when the wind is not blowing. Most of the time that is like saying that they test when the earth stops rotating ;-)
One final bit of advice: If you want different results, you have to change something that you are doing. So often, I see shooters "trying harder" and doing the same failed tests over and over. Also, trying to work up loads with a rifle that has not been properly bedded is, more often than not, a complete waste of time. If you can find a mentor, that is clearly getting the results that you desire, this would be a very good thing. Over the years I have benefited greatly from the advice of my shooting betters. They have been very generous with their time.