I may as well give you the whole enchilada so you have enough info to feel comfortable with this subject.
Parting tools come in HSS, HSS-cobalt, inserted carbide and home made tools. For most hobby applications, HSS or cobalt tools suffice. Inserts work, too, but tend to require a more rigid lathe and set up. Depending on the configuration of the insert holder, it may be limited in depth of cut or may be on the wider side compared to HSS tooling.
My personal bias is for the P-type blades with a flat top. These tools are typically ground with a 5 degree side relief on both sides and, as mentioned, a 7 degree front relief angle works really well. I grind these flat across the front; done well, the tool will not steer. If you are concerned about keeping the blade perfectly vertical while grinding it, simply install it in the tool holder and use that to keep it flat and stable on your tool rest while you grind. I do it this way.
Sharpening these tools requires a light touch because they cut very fast and it is easy to turn the tip red hot if you go too aggressively. Grind a little, cool it in water, grind some more until you grind the whole front. Again, you want to grind until you have an even 7 degree bevel under the front edge and raise a little burr across the top of the tool. Then hone it gently, keeping the top of the tool flat on your diamond stone. You are trying to get rid of the burr, that's all. Done well, you will not see any light reflecting off the edge of the tool. In use, if you see light reflecting off the edge, hone it. If the edge is beat up or chipped, regrind it. You can typically go for months in a hobby shop without having to regrind the tool. My current P1-N blade is now well over 25 years old and is very nearly its stock length; it cuts with no issues whatsoever.
You will see these tools called P-type or T-type blades. They are functionally the same but the cutting element may be shaped a little differently. Some come with flat tops, some with V's and some with a scoop or concave shape on top. Personally, I much prefer a flat topped tool as it cuts predictably for me.
Parting tools are form tools and the bigger/wider it is, the more cutting force it generates. P-type tools are built like a girder or T-beam and are very rigid. I don't worry too much about how far I extend the blade from the holder because it isn't that critical; just get it out far enough to reach center or more. Supposedly, the bigger the work piece, the bigger the parting tool you should be using. This is because the bigger the work, the more extension you need to reach center so the thinking is that you need a bigger tool to reach out that far. There is some logic to this because we know that greater overhang results in greater deflection. However, as I said, a P-type tool is built like a girder and can extend farther than you might expect. For work up to about 1", a P1 or P1-N works well. From 1-2", a P2 is good. From 2-3", go to at least a P3 or 4. They are all ground and used the same way.
Using form tools, including parting tools, is a high pressure situation so lubrication is important. On soft stuff like aluminum, WD-40 works fine. On mild and medium carbon steels, cutting oils works well. For stainless or higher carbon steels, I prefer to use sulfur bearing oils because I am using more feed pressure to maintain a continuous cut and reduce work hardening. On Delrin, nylon, brass, bronze or cast iron, no lubricant is needed.
For speeds, I don't get all that fussy. I usually run at about half the typical turning speed for the material. As long as I can feed fast enough to keep up with the speed and produce a continuous chip, I'm happy. This applies when parting from the front. If you part in reverse with the tool mounted upside down in front of the work or with the tool mounted upside down in a rear mounted parting tool holder, you can go much, much faster and part much, much easier without any digging in or chattering.
That should give you enough info, I hope. Look into a height gauge for your tools. Lots of folks believe that tool height is not a big deal but IMHO, it is. Lathe tools are meant to work best when the tool tip is on center. A height gauge simply allows you to do this very quickly and precisely every time.