Wood – what type of glue do I use

You took the wind out of my sails with that last paragraph. I was going to suggest using a nut/bolt.

As far as it causing problems when the tabletop is lowered, you can recess the bolt head. Yeah, you could make the cavity in which the bolt will stay on the underside of the tabletop, but maybe you'll drill too far or crack/scratch the tabletop if you chisel it out. It could end badly... which is why you should instead house the bolt head on the top-side of the cross member.

Brown = table top
Black = underlying cross member

The one on the left is what you were talking about. The one on the right is what you want to do.

Also, use a washer under the bolt head, etc.

Why not Maple or Poplar? Poplar is very cheap but pretty soft; Maple is harder and pricier but still not terribly expensive. Both take paint well because they have tight grain that doesn't need to be filled to get an even, unblemished surface. You could even go super cheap and use something like Pine, as long as you fill the pores with a wood filler and sand it flush before painting. None of these stain as well as more expensive woods like Oak, but it seems staining is out of the question for you.

As Rl Swamp Yankee said, wood is wood (at least in that the vast majority of it will support your top if the base is built correctly). Any furniture grade lumber can support quite a bit of weight, so go with a grain that will fit your needs. To reassure you, Poplar is used frequently as a secondary and support wood in furniture projects, and Maple is often used to build 300+ lb work benches.

Here's an interesting overview describing wood's ability to carry loads:

http://www.ehow.com/info_12003543_load-bearing-properties-common-woods.html

And a link for calculating the load-bearing capacity of a column of wood (although this looks like it's only for typical construction-grade lumber rather than hardwoods):

https://courses.cit.cornell.edu/arch264/calculators/example7.1/index.html