There is no antibitic that can kill all the bacteria, in particular these associated to sediments and particles due to protection of those provided by organic and inorganic matter of the particles. No antibiotics (unless thy are at very high concentrations) will damage phytoplanctonic eukariots. You may try to arrest (not kill) bacterial development by using antibiotics of two different groups, eg, tetracyclines and macrolides, their concentrations you will need to establish experimentally.
It depends of the concentration of the antibiotic. The antibiotics can be active against the bacteria G+ and G+ at concentration higher than that used in human. May be the antibiotics used in cellular culture could be effective ? Ampicillin 2.5 mg/L (cytotoxic at 30 mg/l), Erythromycin or gentamicin at 50 mg/L (cytotoxic at 300mg/l) and so on.
I have used both Gentamycin and Kanamycin to eliminate symbiotic bacteria from marine larvae and juvenile organisms. If you have a sample of suspended communities, and not packed particles, you should be able to eliminate many of the bacteria. What is the goal? Which phytoplankton are you trying to keep? There are many phytoplankton that are bacterial as well as the eukaryotic. In my experience, tetracycline was toxic to marine eukaryotes (well, metazoan), and may also be toxic to the planktonic eukaryotes.
To determine the correct concentrations, you will have to test them. For larvae they tolerated up to 100 microgram per ml. Gentamycin to eliminate bacteria. But for smaller planktonic organisms this may be lower. Chloramp is also toxic. Ampicillin, kanamycin and Gent were all tolerated well by marine larvae, suggesting other planktonic marine organims may also tolerate them.
If you want to maintain the cyanobacterial population, look in literature for antibiotic tolerance of the cyanobacteria. In general, this will be tricky. Consider carefully what your question for the experiment is, or what the goal is. There may be a way to accomplish what you want without treating with antibiotics.
I agree with Seana, which antibiotics to use and at what concentration will be dictated by the species you are trying to remove and the species you are trying to keep. I would recommend finding research articles that developed methods to isolate the same types of species you want to isolate. Once you compile a list of methods used by other people, you can start to test which method works best for you.