We generally have cut back on nut butters because for our health objectives they are too handy to have on hand!
Be patient with nut butters, it takes a longer time than I would expect.
Peanuts goes to peanut butter in my food processor and it takes a while to get there, no added oil.
Walnuts goes to a spreadable walnut butter but it has texture, again in the food processor w/o added oil I rarely use it but if I do it is for crackers because crackers won't get crisp without at least some nut butter (we don't use refined oils).
Almonds would be tougher to get into a butter like state. They seem to be more fibrous and less oily.
I make a salad dressing with sesame seeds (but tahini would work too). Soak the seeds in hot water, drain, then make the dressing in a blender, adding water or vinegar as a liquid. They pulverize and emulsify the dressing.
If using raw cashews, they also benefit from soaking to use in recipes.
I have a low cost food processor, large, Hamilton Beach. I also can use a metal cupped nut and coffee grinder for smaller amounts. I use an oster blender.