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Beetles seem to be used a lot for this sort of study. Flies would be good too, but there seem to be fewer studies using them.

You need to employ several methods of trapping to ensure you get the widest range of species. It is virtually impossible to come up with meaningful quantitative population figures for a species - you can really only give numbers of a species caught in relation to total numbers of individuals caught. It is possible to express an opinion of a species status based on your own and past records, but with many species it can be little more than a guess.

Some useful literature:
Environmental Monitorying, Surveillance and Conservation using Invertebrates - M Eyre (ed) 1996, Newcastle, EMS Publications - lots of good stuff, but some outdated. A series of case studies - some published elsewhere also.

Ecological Census Techniques: a handbook - W Sutherland (ed) 1996, Cambridge, CUP.

Handbook of Biodiversity Methods: Survey, Evaluation and Monitoring - D Hill et al, 2005, CUP

Invertebrate Surveys for Conservation - T New, 1998, Oxford, OUP.

Fowles, Alexander and Key - The Saproxylic Quality Index: evaluating wooded habitats for the conservation of dead-wood Coleoptera - The Coleopterist 8(3), 121-141

Quantification of Conservation Criteria using invertebrates - M Eyre and S Rushton, 1989, Biological Conservation 26, 159-171

I think the minimum number of trips is 3, timed to peak periods throughout the year eg May, July and Sept/Oct. It isn't really enough, but it is a start and will give you a reasonable range of species, and provides a stepping stone for someone who comes after. To make the study really worthwhile you need to be able to return year after year.