There is a minilab forum out there somewhere. I only consulted with them a few years ago but forgot the url.
I used to be an AgfaLab maintenance tech and this idea is feasible (a guy at an old lab I used to work at had built his own C-41 machine) but makes my brain hurt when thinking about making my own system.
Basically, you need to worry about light-tightness, water-tightness, transport consistency and temperature consistency.
I think a good material to use for the main side/tank supports is lexan or very thick plexiglass. Both are easily machined and can be precisely drilled. You're going to need some tanks which can withstand the chemistry. No sealants like silicone will work. This is where rubbermaid comes in to play.
The individual roller transports themselves are not too complex to make by yourself but there are so many pieces and the precision has to be perfect. If you don't mind using other parts, you can save a lot of headaches by sourcing a few of the shallow tank transports. If you use the Agfa ones, you'll need a 1/4" wide bicycle chain to pull them along. This is kind of the cool Rube Goldberg part. You can do a flywheel governed manual transport which you would spin up yourself to a minimum operating speed. You could also do a direct-drive one which could be operated by hand as well. For both of these you would need to do a gear reduction since the film itself moves through hot C41 chemistry about 3"/second and keeping that kind of consistency by hand without a gear reduction is almost impossible. The flywheel part is to help keep it rotating the same speed in case your hand or arm gets lazy or shaky or whatnot for a bit.
The temperature can be regulated by 120VAC fluid heaters. These are found cheap on ebay or chemistry supply outlets and there is little to go wrong with them even is used. They either work or they don't.Pick your desired operating temperature, buy a few then figure out where in your tank to hook them up. To regulate them you'll need a thermostat or for short runs you can just use a regular chemistry thermometer but it has to be long. These tanks get a bit deep and without a circulating pump the chemistry temperature can vary a lot between the surface and the bottom.
If you think ahead you'll be able to do black and white in this machine as well. Would only take a small amount of heat to keep your chemistry consistent.
If you keep it really simple with no valves (other than a petcock at the bottom of each tank to drain the system) you'll have no problems with algae. After draining, just wash each tank out with clean water and you'll be good to go. Once in a while clean with a 1/10 hypochlorite solution to keep everything sterile.
As for the dip and dunk, don't even go there. They are beautiful machines and when they work, they provide amazing results. Problem is they need a whole garage-sized darkroom dedicated to them since the transport has to fully pick up the rolls and move them from one tank to the next.
I began my professional film development career on a dip and dunk machine. While it was more of a pain to regulate and operate than the roller transport, it gave better results since nothing ever touched the film and there was little chance of something jamming a roll.
Good luck!
Phil Forrest