You have things summarized fairly well, but your project needs are rapidly increasing your budget, I think.
If you want a scripting capable autopilot that requires minimal soldering, the price point goes up. Look at the QioTek ZealotH743.
If you want to forego a computer running GCS software and operate solely with an RC transmitter, you’ll want one that can display some information (see Yaapu telemetry). The Radiomaster TX16S fits that description quite well. While cheaper options may be available, I wouldn’t recommend them for the use case you’ve presented, and the TX16S is the least expensive radio of which I’m aware that supports the feature set you’re going to want.
Waypoints can be recorded using the Save Waypoint RC option. While it isn’t included on the documentation page, all waypoints can be cleared by toggling the assigned RC channel while the autopilot is disarmed.
The “advance-wp” script from the first post in this discussion can be used to cycle waypoints. For your use, it should probably be modified a little to include a message that indicates which waypoint is selected along with a feature to recycle to the first waypoint index if it can no longer advance forward.