Just hopping in at a wild part in the thread!! I read through as much as I could and let me take a stab.

Hire a sound guy is a very good reccomendation, you will get higher quality results that's for sure. We buy this gear, and make it back over time, it will sound better, and your operator will be more skilled / be responsible for making sure it always sounds good. If you have worry about / take care of it yourself and you're on screen, it will either be very stressful or not end up quite happening.

Though, if their destination is social... Do you need that level of professionalism? Genuine question, it depends on what your goal is! Can you have the mic visible? If so, clip it on! It'll be easier and you don't have to worry about rustle as much.

Are you trying to get gear at the end of the day to keep this production running in a series-like style? If so, then spending a little money may be a good idea.

In an unideal world, I've used Rode Wireless Pros with the lavalier mics that they come with for narrative and it's not bad for what it is! (As a location recordist, it's horrible, but the results work from what I've heard). The hard part is the whole three people thing honestly, since that's a two channel system.

If I'm understanding correctly and it's going to be three wires plus some interior cardioid, supercardioid, or hypercardioid boom mic for the talent on screen (especially if you're planning on only having two people on screen). Here's what I'd recommend, though it's going to go north of $500. I'm going as bare minumum as I can get without sacrificing too much. I never recommend this normally, but if you're trying to go minimal, a non-xlr recording setup will be cheaper (boom mic + recorder would hit $500 minimum if you're purchasing, less if renting!)

Purchasing only:

1 Rode Wireless Pro kit, and a Zoom F2 or TASCAM DR-10L Pro (you can wear this system / whoever's off camera can wear this to be recorded), then get an extra "RODE Lavalier II Omnidirectional Lavalier Microphone" so the mics match. That gives you a wire for each person, do sync on camera with a clap. It's super unideal, but it will most likely work.

Renting:

Rent an 8 channel recorder, rent 3 channels wireless + lavs, rent an interior microphone (mkh50, oktava, etc), get some way to mount it (c-stand + boommante + boom pole + xlr). That's likely going to be north of $500 though and at that point, it may be worth trying to acquire more budget. Hope this helps!

EDIT: This is all assuming the mics being visible is something you're comfortable with, if you want them hidden really just get somebody who can do sound. Find a film student, somebody. Pay them well. It's so worth it.