It's true that many of us go through a progression like this, but I wouldn't really call it logical, and it's certainly not efficient. If you know what your long run goal is, I'd try to get there with as few intermediate steps as possible.
If your eventual goal is an eHERMS, just start with a manual gas-fired HERMS. If you don't already have one, I guess you'd need a pump. But otherwise it sounds like you already have access to a cooler, a keggle, a gas burner, and an immersion chiller -- so you have almost everything you'll need. (You can just use your friend's immersion chiller as your HLT coil.)
EDIT: Rereading your post, I'm realizing you're not 100% sure what you want your final system should look like. In particular, you have both 2-vessel Brutus 20 systems and 3-vessel HERMS along your upgrade path, which are very different setups. Once you get a pump, I'd recommend trying both with the equipment you have to see what you prefer. In fact, try BIAB and direct fired RIMS, while you're at it. Once you've experimented and know what your ideal system looks like, it'll be a lot easier to think about the best upgrade path for automation.