there are three very recent short papers you should look at immediately if you are interested in non-string QG and Quantum Cosmology (QC)
Bojowald
The Dark Side of a Patchwork Universe
http://arxiv.org/abs/0705.4398
this gives a 7 page description of "the universe according to loop quantum gravity"
pages 3 - 10, of which the first 3 pages give a GENERAL outline of the LQG approach he needs for cosmology
and the other four pages a specializing it down to the quantum model of the universe.
the other two you should look at are a couple of recent ones by Ashtekar, one is introductory for beginning researchers, the other is a survey talk invited by a major international conference and intended as an up-to-date review for specialists in other fields.
An Introduction to LQG through Cosmology
http://arxiv.org/abs/gr-qc/0702030
"This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how `emergent time' can arise; ii) how the technical issue of solving the Hamiltonian constraint and constructing the
physical sector of the theory can be handled; iii) how questions central to the Planck scale physics can be answered using such a framework; and, iv) how quantum geometry effects can dramatically change physics near singularities and yet naturally turn themselves off and reproduce classical general relativity when space-time curvature is significantly weaker than the Planck scale.
20 pages, 4 figures, Introductory Review. "
Loop Quantum Gravity: Four Recent Advances and a Dozen Frequently Asked Questions
http://arxiv.org/abs/0705.2222
"As per organizers' request, my talk at the 11th Marcel Grossmann Conference consisted of two parts. In the first, I illustrated recent advances in loop quantum gravity through examples. In the second, I presented an overall assessment of the status of the program by addressing some frequently asked questions. This account is addressed primarily to researchers outside the loop quantum gravity community.
21 pages, to appear in the Proceedings of the 11th Marcel Grossmann Conference"
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STS I would advise you to download these, print them out, and look them over, whether or not you think you can understand them. It will give you a very useful up-to-date impression of what the field is about.
There is TECHNICAL progress (possibly quite important) happening in other areas, like spinfoam models including matter and Feynman diagrams of particle field theory.
But the most visible aspects of what is going on in have to do with cosmology. there are rapid developments going on in QC (quantum cosmology) and to some extent they may begin to influence the rest of quantum gravity research.
It is highly significant that Ashtekar chose to INTRODUCE LQG by way of its applications to cosmology. This is pedagogically a smart choice because you see interesting applications right away.
In its classical form, cosmology uses a SIMPLIFIED version of Einstein classic Gen Rel---simplified by assumptions of symmetry and uniformity, so there are only a handful of variables and parameters to worry about. Analogously quantum cosmology uses a symmetry reduced model which is much simpler than the full LQG theory. Fortunately the universe seems to be fairly uniform at large scale and so one can do this, and it makes the whole business more intuitive and comprehensible.
So again I would strongly advise having a look at these three, short, recent papers----to get an idea of what Loop gravity and cosmology folks are really up to.
String is a totally different story. I wouldn't try to study them simultaneously because in practice (what the leading researchers are actually working on) they are very different. After a while you might begin to make comparisons contrasts analogies at various levels and in various corners and subdepartments.
But to begin by trying to understand in tandem would be, I think, a systematic error.
