Best of luck to you as you treat these infections. It will vary depending on which organisms you are taking on. Doxy is typically a good abx for most tickborne infections, however, it is hard on the gut so be aware of that as well it makes your skin sensitive to light and you will burn easily. it is effective on the Borrelia spirochete though.
Now intracellular infection like Babesia is an intracellular parasite so many MD's will treat with a drug like Hydrochloroquine otherwise known as Plaquenil.
With also having Bartonella it can be difficult to treat so many MD's will pair up abx rifampin is a common one that is used for Bartonella.
I would make sure though that you start off with one and let your body adjust and add in the others in a staggered manner and make sure you are detoxing and taking plenty of probiotics 50-100 billion units a day about 2 hours after abx is a good place to start.
Your regemin may vary as well do you will have to see how you respond with treatment but these things do take time. My regemin was a combo, I started on minocycline, Rifampin, and Plaquenil. and my second course was Flagyl and ceftin. once you stop improving on one then you may need to switch to a different combo until you are symptom free and then treat for another month or so.
Just know it will vary from person to person and MD's may use different combos but keep keeping on, and good luck.
Hope this helps,