As i am working on the similar field, i would suggest you to go with a trail and error method for a best result also that data will be very valuable for further research work and also publication.
When antibacterial activity is our prime concern, you can always opt for Hot extraction method like Soxhlet extraction with various solvents. Solvents also, trail and error will only work out if your plant sample is new or something that hasn't been intensively worked on. For the solvents that you can use solvents with varied polarity. for eg, start with water, 70% ethanol, methanol, ethyl acetate, petroleum ether, hexane, chloroform etc. try to do extraction with these solvents and u can select based on the yield also.
If you are going to perform the test invivo (on animals), it is preferable to prepare an aqueous extract (decoction or infusion).
however, if you are going to study the antimicrobial activity in vitro, you can use a cold maceration (at room température) with methanol or ethanol at 80%
First of all defat the leaves by extraction with non-polar solvent(n-hexane or petroleum ether) then use more polar solvent ethyl acetate, methanol and 70 :30 methanol:water.Check with TLC and evaporate the solvent ,fanally evalute their biological activity