Sorry Em, I've been guilty of doing a thing that really peeves me...assuming you are clairvoyant in my answers.
Truth is, I use almost all glues at some stage, but NEVER tube polystyrene cement. The liquid glue I use is 'Tamiya Extra Thin'. It comes in a glass bottle with a green and yellow label. It's like some kind of spirit in consistency and evaporates quite quickly...this means a session glueing fuselage halves can be interesting. Of course it responds really well during the kind of application where you join two parts dry, then allow capilliary action to spread the glue. Really good...you just have to touch the brush (the one inside the lid) and it runs up the seam very well. I only ever used the provided brush. I have a Testors liquid one that is way more viscous that I use sometimes...if I need to glue larger areas...it evaporates more slowly.
As for CA glue (super glue) I've always just used whatever was cheap at the super market. I'll use CA for PE or for anything that I need to 'grab' quickly. Being quite brittle, I always wait for my CA to cure, then re-glue the join with white glue to reinforce the join. Elmer's is fine. Biplane rigging is a perfect example of the 'double-glue'.
For styrene to styrene joins, I use the Tamiya if I can because it's the strongest bond. CA grabs fast but is brittle and white glue shrinks when it dries and isn't great for styrene...it needs some 'tooth' and styrene is smooth. The only 'specialist' glue I have is in a plastic bottle similar to the black one pictured above. It has a purple label and is designed for clear parts such as aircraft canopies. CA glue can 'fog' clear parts. It's sticky stuff but slow drying and it dries crystal clear.
Hope this has been more helpful mate.
Peace.