Butter sauce: There are of course many different butter sauces. For a while the "hot" butter sauce among chefs was the beurre blanc, in which you make a flavor base (e.g. white wine, tarragon, cracked pepper, reduced to a syrup and strained) and then start whisking in whole butter, a piece or two at a time, over low heat. This produces a thick yellow-white sauce with an admirable purity of flavor. The down-side, of course, is that it's a great deal of butter per serving. It is quite wonderful with fish and shellfish -- I don't know if that counts among the "meat of any kind" that you don't eat?
There is also a buttery pan sauce. Deglaze the pan you've cooked things in, using an appropriate wine or stock or another liquid that reduces well. Cook the chunks in the liquid until the liquid is well reduced, strain fine, and then over low heat whisk-shake in several Tb whole butter until glossy. This process of montant au beurre gives richness and body to a simple deglaze. It works extremely well with anything that throws a significant amount of caramelized material, including root vegetables and onions.
Sabayon: I think the central sauce-base you're missing in your list, for your purposes (given the absence of meat, I mean), is the sabayon. This is a "mother sauce," which can be flavored in a vast number of ways. To make a basic sabayon, if you've never done it before, I suggest starting by doing it the right way -- but allowing yourself maximal leeway for difficulties. Put 4 egg yolks in a medium slope-sided skillet or another medium-sized pan or pot into whose bottom corners you can reach with a whisk (a straight saucepan is the most difficult). Add 1 Tb cold water per egg yolk. Melt 2 sticks of butter and leave to one side; if you wish, you can clarify the butter (skim all foam, then ladle the clear butterfat into a pourable measuring cup, leaving the white milk solids on the bottom), which makes a thicker sauce at the cost of some buttery flavor. Have on hand some acidy flavoring: lemon juice, herbed reduced white wine, etc.; just a few Tb is sufficient, but I always assume that one should have available as many Tb flavoring as egg yolks, though if you use it all it will probably be too strongly flavored. In the pan, without heat, whisk the yolks and water very fast, about 30 seconds, until foamy. Now turn the heat to medium-low and continue whisking medium-fast, being sure to get into all the corners. As the mixture gets warm, it will begin to thicken. Keep whisking without stopping. Quite suddenly, it will turn almost white and very thick, and you will be able to see the pan bottom easily between strokes of the whisk. Whisk as fast as you can for another 20 seconds, remove from heat and whisk another 20 seconds. Now you have a sabayon base. Whisking steadily but not over-fast, add the butter medium-slow -- you don't have to be super-slow about it, because you've already got a strong emulsion and just have to make sure not to break it by adding everything at once. When the sauce is as thick as you want it to be, add a pinch of salt, then add the flavoring a little at a time. Keep adding and tasting until it's right for you. If you add only lemon juice, you have Hollandaise. If your flavoring is white wine, tarragon, shallots, and cracked pepper, you have Bordelaise. And so on: add tomato paste to this and you have Choron. Note that you don't need any fat, and that you can use olive oil (or whatever you like) in place of the butter, and so on; each variation will produce a different sort of sauce. Once you've made a few sabayons, you will see that it is simple, quick, and can be quite healthy -- certainly as compared to beurre blanc. The sabayon base, with or without any admixture of fat, can be extremely light, particularly when you use a light, simple acid like a citrus juice, and the result is excellent with seafood and a wide range of simply-prepared vegetables (think asparagus for a classic example).
Beyond this, you might consider buying a copy of James Peterson's Sauces. It's a big book, and not cheap, but the range of sauces he explains -- and the depth of his explanation -- should keep you busy for a long time to come.