Not poly for sure, it contains cobalt and zirconium dryers. Permalyn contains no heavy metal dryers but does have MEK, Benzene, and Xylene in it which are necessary carrier/solvents for polyurethane.
Any tung oil or linseed oil based finish will work. Some are better than others. If you want it to build up on the surface, you will need a product that contains varnish resins as well as drying oil.
Basically you have three choices: Linseed oil, Tung oil, and polyurethane as a base oil. Then you have several resin choices, the most common and cheapest being alkyd or phenolic resins, though there are many others like copal, pine, mastic, shellac, etc. Polyurethane is technically a synthetic resin, not an "oil", but in practice the poly and its solvents act as both an oil and resin together. Most finishes have a carrier solvent, basically mineral spirits which aids application by brush or spray. Hand rubbed finishes do not require a solvent, nor is one desired except possibly with tung oil which tends to be about like honey in its raw state and can be difficult to apply.
The vast array of finish products and recipes are a result of combinations of the above things, so the important thing when choosing a finish is to decide what you want it to look like, what you need it to withstand, how you are going to apply it, and choose a product with ingredients that fill the bill. It's kind of like patch lubricants and cleaning solutions, everyone has a favorite, they're all different, and the particular method of use/application has more to do with good results it than the product itself.