Suggested power-tool and attachments to remove rust from a BBQ pit
Wire brush and sandpaper.  
Hi-temp paint for grills. 
Repeat as needed. 


Also, be careful what strip/rust-remove/paint chemicals you use.  Many will play rather quite badly with heat and/or food. 

As far as a cordless, battery power tool to do the job, good luck. I do a LOT of rust removal. Looking at that, it looks like 90% hand work even with the tools I possess.  Your only option here would be media blast, and you won't be able to lift a battery that will power that.  This is the core problem with battery powered rust removal: the energy requirements are too great.   This regularly hamstrings me because I have a lot of rust removal to do in places with insufficient AC power to run a compressor.  Fortunately, humans are endurance hunters. 

Even more than that, I am concerned that younger people feel entitled to "go straight to power tools". This misses an important point. The problem is, you really need to use hand tools to get a tactile feel for how materials and tools actually behave, and the real challenges of working with the work. If you haven't hand sawn through a knot, you won't understand why it's so dangerous when a circular saw hits one.  If you haven't hand wirebrushed a complex shape, you'll quickly destroy a power wirebrush and quite likely injure yourself. Whereas you are vanishingly unlikely to do serious harm with a hand tool.  People my grandfather's age are long gone; but they would have told you this.  You should graduate to power tools only when you have "earned your chops" with hand tools. 

In this case, it also hobbles you from accessing the work you need to access: If you showed up to this job with only power tools, you will not be able to do the job.