These are the handling agents at BHX, and the airlines who I think that they handle, though I'm not completely up to speed with contract-by-contract blow-by-blow accounts;
Penauille Servisair
Aer Lingus, Air Berlin, Air India, Air Malta, Balkan, City Airline, Continental Airlines, Emirates, European, Excel, Neos, PIA, Thomsonfly
aviance
Air France, Astraeus, Austrian Arrows, bmibaby, bmi charter, BritishJet, Eurowings, KLM, KLM Cityhopper, Lufthansa, Ryanair, SAS, Thomas Cook, Uzbekistan Airlines
Swissport UK/Groundstar
Aerosvit, Air Slovakia, Cyprus Airways, Eurocypria, First Choice, flybe, LTE, Mahan Air, Monarch Airlines, Monarch Scheduled, MyTravel, Swiss, Turkmenistan Airlines. (Swissport are likely to get the contracts currently handled by BA - SN Brussels Airlines and Eastern Airways, alongside the BACON flights after the flybe merger.)
Aviation Support
HLX, SkyEurope
I would say go for the company that you can imagine yourself working for. If you're looking for something very fast-paced and busy, then Swissport might be for you. I have experience with aviance who are my airline's handling partner at BHX, and they are very professional.