So called Danish oil or Swedish oil or whatever Scandinavian oil, finishes, are actually what could more correctly be called 'long varnish'. That is, a type of varnish that has a very high oil content.
I've used them a lot but usually bump up the solids content by adding 20% polyurethane to make it a little more substantial.
By the way, it'll say on the can that you need to apply 2 or 3 coats. That's a way to get you to use up more product. Put it on heavy and leave it sit for 10 minutes. By that time the wood has soaked up all the oil it's going to. Wipe it down lightly. That is to say, don't scrub it dry, just give it a wipe to pick up the excess. Next day if you want you can rub it out with super fine steel wool. Depending on the wood species, there may some little globules of oil seeped back up to the surface that need to be dealt with and the steel wool works well for that. (You will have sanded to at least 220 grit before applying the oil.) Watco and Behr are both good brands.
The coloured oil stains work great on certain woods and spell disaster on others. Open grain woods like oak and ash take these oil stains wonderfully. Birch will come out blotchy.
Anyway…. that's my 2¢ on oil. I've used many a gallon.
Personally I'm not fond of polyurethane (varnish) because of it's slow drying time. The longer a finish takes to dry the more dust it will pick up from the air. However I know woodworkers who use it a lot to produce wonderful tough, glossy finishes, like guitar makers for instance. My understanding is that it takes a lot of coats and a lot of polishing.
I've sprayed quite a lot of lacquer over the years. Not so much anymore. Goes on easy, dries quick and smooth, can be re coated almost endlessly since each coat 'burns' itself into the previous one but it's bad environmentally, not very water resistant and you need a respirator.
Not to be overlooked tho are the spray cans of solvent based lacquer that cab give you a very professional looking finish with very little fuss on small items.
I've also used quite a lot of waterborne clear finish. It has it's pros and cons.
I think the best advice I could give is, try them all and keep in mind that other than oil, which is dead simple, very forgivable and for the most part really easy to fix up….
applying a good finish is a skill that takes practice.
Watch a few youtube demos on each one before you try it.
Like Ralph said, there's no one finish that's appropriate for all projects.