Best masters program to get a start in management consulting (MiF vs MiM)

Hi everyone,

I've decided that I want to pursue a career in consulting and I'm wondering which masters program will best enable me to get a position at MBB or a lesser consulting firm.

I'm considering an array of MiF and MiM programs in Europe but I'm not sure which programs will give me the best chance at recruiting for MBB. The schools I've looked at are LSE, LBS, HEC and St Gallen all of which offer MiM and MiF programs. Im also interested in the Oxford MFE and the INSEAD MiM. Do you guys have any thoughts on which programs I should apply to and which degree MiM vs MiF is more sought after for consulting.

Apologies my post seems a little scattered I've just found a lot of conflicting info online.

Thanks

P.S. Here's my background if it helps.

Undergrad - BA International Business Double Degree - I've just graduated and am struggling to get a job.

GMAT - I'm taking the test in a couple of weeks and expect to score 750+ with a high Q score.

Work Experience - Currently just an 8 month internship as a Risk Analyst at a Fund Management Company in Luxembourg.