I like to separate your question into 2 sub-questions:
#1 How do we determine which side to charge?
#2 How much is the right amount to charge?

On #1, my answer is that you can charge the side(s) for whom you add the most value. In your examples, Uber really solves a big problem for drivers, it's that they sit idle for a good part of the day, so are willing to pay a lot for new leads. (their alternative is no work) Consumers are charged more for the convenience of a private car but they are probably not so much willing to pay more for a taxi, even if they can hail one from their phones.
For AirBnB, it's a mix, it's a way for landlords to monetize idle capacity which they are willing to pay for, but it's also a way for a renter to pay less than they would normally pay for a hotel.

On #2 (how much), I like to triangulate a number of factors:
- What's the maximum amount I can charge one side, while still being a good deal for them.
- How much do I need to charge so that I can become profitable? (the economics are quite different if you charge 3% vs. 12%)
- What are comparable services charging for substitutes/competitive offerings?

I will just add that there is no formulaic way to determine pricing strategies (curated vs. open), and it's a lot more about what's the comparable and what the value delivered is.

That's how I approached the question while deciding the business model at ProBueno.com (my startup)

You will find a lot of different views on equity split. I haven't found a silver bullet. My preference/experience is for:
1. Unequal shares because one person needs to be the ultimate decision maker (even if it's 1% difference). I have found that I have never had to use that card because we are always rational about this (and I think us being rational is driven because we don't want a person to always pull that card cause it's a shitty card to pull)
2. When it comes to how much equity, I like Paul Graham's approach best: if I started the business by myself, I would own 100% of the equity; if xxx joined me, he/she would increase my chances of success by 40% (40% is just an example) at this moment in time. Therefore, I should give him/her 40% of the company (http://paulgraham.com/equity.html)
3. In terms of range, it could go between (15-49%) depending on the level of skill. But anything less than 15%, I would personally not feel like a cofounder
4. Regarding salary and the fact that you will pay him/her, that's tricky but a simple way to think about it: If an outside investor were to invest the equivalent of a salary at this exact moment into the startup, what % of the company would they get? (this may lowball it if you think the valuation is high but then again if you think you could get a high valuation for a company with no MVP, then you should go raise money)

One extra thing for you to noodle on: given you are not technical, I would make sure a friend you trust (and who's technical) help you evaluate the skill of your (potential) cofounder. It will help stay calibrated given you really like this person.