Well the best stuff is CA (super glue) and the key to it is to use very small amounts, applied using something like a cocktail stick, or a pin etc. Put a drop of glue on a scrap piece of plastic and transfer it to the place on the model you want the PE part to stick to, then using tweezers place the PE part and (hopefully) it will stay were you want it.
It is important to wash the PE parts first using IPA or some similar solvent to get rid of any remaining masking solution or grease, this will help the part stick. Some people recommend heating the part with a flame (annealing), but that is not usually required with modern PE parts., as these days the brass is pretty soft. (early PE sets were made from quite stiff, thick brass)
Parts should not be painted first, as the paint will stop the part from ticking to the model, you will find that you have a nice piece of paint glued in place, and that the PE part just falls off!
This will also go for your solder, although you could try drilling .010 or .011holes where you want to locate the ends, and this will make fixing the solder much neater as you wont need very much glue, the solder should be pretty much an interference fit in the holes.
I hope this is of help.
Phil