OK, now we're talking.
For brew rig design, lifting anything heavy is a pain - even potentially dangerous. Manual sparge with a bucket is doable, but also a pain. If you're going to build a rig, may as well go all out.
So you need to get sparge water from the HLT to the MT, then wort from the MT to the BK. That's two steps, requiring either three tiers or a pump(s). Three tier would be HLT gravity down to MT gravity down to BK. With a pump you could do two tiers which might be HLT gravity down to MT and pump to BK. With two pumps you can do a single tier, pumping from vessel to vessel.
When you're looking at your kettle conversions, you need to figure out a couple of things. IMO, false bottoms work best with direct fire mash tuns. This allows you to stir without crushing the other filtering options (ss braid, bazooka, etc). Those options will however work just fine, depending how you heat, if you step mash, and how you sparge. I'm not going to talk about sparging, it will raise an age old debate which you can search for all you want...probably not productive now.
For the MT you'll need a ss coupler (welded or weldless). Inside connection would some sort of pickup tube (many options here) and a false bottom (several options here). Outside connection would be a ball valve.
For the HLT, all you really need is the coupler and ball valve, though you might choose a pickup tube here also to avoid a gallon or so of residual water.
For the BK, you need the coupler and ball valve and some sort of pick up tube. Some brewers will also user a filtering device here (bazooka t, stainless scrubby, hop taco, deflector plate, etc). I choose to whirlpool, concentrating a hop cone and minimizing hops/break material in the fermenter. Again there are many choices here and they will dictate which parts to buy.