A space elevator, 'going up!'

You said:What will determine what weight (assuming the cable strength is not the issue) can be hoisted into space?

Unfortunately that's an assumption that cannot be made. I read an article several years ago stating that any currently available material would break under its own weight. As I said it's been awhile and they may have been discussing conventional wire ropes, however nano tubes were mentioned.

I did a quick Google for space elevators and there's a wealth of information available, so if you haven't done a search for you might want to start their. They also discussed the weights that could be hoisted.

But don't be disappointed, even the nano tubes have not proved to be strong enough.
If you have a stronger material, let me know, that would be something worth investing in.
When that one little hick up of material strength is resolved, goodbye a rocket launches. Http://en.wikipedia.org/wiki/Space_elevator

This subject was handled very well in the last 30 - 50 years in hard science fiction and science in an overlapping fashion. No particular title comes to mind right now, I am sorry it was over a decade I had one of them in my hand. But, they are out there, quite a number of them presenting respectable physics. So search, and Ye shall find!

Make your elevator from a strong flexible tubing with holes a motor can use to climb up and down.

Naw, it is not that simple. A cable from ground up to geosynchronous orbit and beyond for counterweight purposes is the basic design. No matter how you taper and shape it, with any material we know now, it will break under its own weight, never mind any payload. If my memory serves well, it was metallic Hydrogen under room temperature(?!?) that has the theorethical strenght. I admit, that was before discovering Buckyball, and tubes with their wondrous capabilities. But, I do not believe, they would match up, not quite....

But, there is a sexier solution. Much more relaxed in material requirements. And, at the same time requires macho piloting skills big time. Now, that is much more my ticket!! It is the rotating cable, that from time to time dips into the atmosphere with its end, slowing down to subsonic. There you (and I mean you!!) pilot the payload up and attach. The cable keeps on rotating, providing you with interplanetary speed. When you arrive at, say Mars, the same system slows you down. All the way they steal energy from the planets, Exactly the same way todays flybies and slingshots are realised.

It takes somewhere 10% of the material volume, and around 20% of the material strenght requirements vs. the stationary beanstalk.

Additionally, Earth's gravity stretches the limits of such a system. Any celestial body with less requirement is actually easy on it. So once we are out of this gravity well, we are home free (energy vise). After all, who want to stay in the crib all the time!?!