Cheap is not the word you want to use. Not all CA glue is the same. Some have different reactions.
You will get all kinds of suggestions and brands.
One thing is you need to get both a thin CA and a med. CA to start with. Do not get too much because it does go bad. It has a shelf life unless kept in the fridge or cool place which will extend it. Do not put open bottles in the fridge. You introduce condensation into the bottle.
The brand I use and have nothing but good success with is
I use the normal superglue from Harbor Freight Tools .... I haven't noticed anything lacking in it so far, other than I need to occasionally re-glue an acrylic barrel if it comes loose on me during turning.