My advice when it comes to stones for honing is the same as it is for brushes - don’t start cheap just to get going, spend a little more to get something worth having long term or don’t get it at all. That said, you don’t have to spend a lot to get started. You can certainly get your feet (Blade) wet with good quality lapping film and a FLAT piece of marble tile that has been cut into 3 inch wide by 12 inch long pieces (that means you can get one tile and end up with 4 pieces...unless one breaks when they cut it like it always does) you can also do 4 inch wide pieces if you want to, some people find film that is already cut to 4 inch wide so a 4 inch wide tile makes sense. Lapping film is consumable so you will have to buy more of it from time to time but it’s fairly inexpensive. Lapping film also has limits as to what kind of heavy work it can do AND it can be cut during use. I kept cutting my film so I gave up but film is capable of great consistency and very sharp edges so it’s worth learning to use.
The pasted balsa strop is an invaluable tool to have if you are a straight razor user, it can take an edge to an all new level and it is a great way to finish any type of honing. The pasted balsa strop is basically just a strip of balsa wood glued to a piece of tile, lapped flat and coated with a small amount of either, diamond paste, chrome oxide or iron oxide. I have several on hand, each with a different type of paste, ranging from 0.10 micron diamond and 0.10 micron iron oxide to 0.25 or 0.50 micron diamond.
Others have already mention some of the synthetic stones, my only Good experience with the synthetics has been the norton stones. I had King stones and a cheaper Naniwa, both did the job fine (king did better) but they are the reason I say don’t buy the cheaper stones just to get started, hold out for a better option. If you can get a “splash and go” rather than one that requires soaking go that route, you will be much happier you did. Don’t waste money or worry about getting a lapping plate, just get an extra 12x12 tile and some wet/dry 600 grit sand paper. I like to have 2 tiles, one with 600 grit stuck to it with a light spray of photo adhesive and one with 1500 grit. I lap the stones flat on 600 then give them a light polish on the 1500. OR you can use a plate of glass and Silicon Carbide grit (again, 600 and 1500 or higher). Synthetic stones are amazingly capable and consistent so if you choose to get good/great quality ones you won’t need anything more.
As for my suggestion about where to start, I think the best place to start would be to Get a good/great synthetic in the 4000 to 8000 grit, maybe even a combo stone (spend the most here) and use lapping film and pasted balsa for the higher grit and finishing work. Build out from there, the super fine finishing stones are terribly expensive and can be worthless if you don’t know how to use them (or have basic skills) so don’t start with the most expensive and work backwards.
MY personal preference is natural slurry stones, they offer a great amount of versatility and value but can also be difficult to learn because of the different variables you have to contend with. A single Coticule with a slurry stone can cost $100 (for a modest sized one) but it can be capable of honing a razor from bevel set to finish if you do it right. There are limits to the kind of sharpness you can get with a coticule but when you combine a coticule with other stones or methods the results can be amazing. The costs of natural stones aren’t bad, you might be able to build quite a personal quarry rather cheaply if the idea interested you.
As far as strops go I tend to make my own. I have some nice ones I’ve been given of picked up along the way but I still like the ones I’ve made for myself. I thought I would like a 3” strop more than I do, truth is a 2 3/4” is far better. A nice 2 1/2” strop with hemp cloth component is my favorite.
