Very General Madrid/Andalusia Questions

1) Public Transport vs renting a car. Budget, convenience, comfort.

For the places you want to go to I'd say public transportation will have it in budget, convenience, and comfort. The only objection would be if you are using Ronda to explore la ruta de los Pueblos Blancos, in that case a car may be more of use for that portion of the trip.

In my head, I see fly into Madrid....Sevilla....Cadiz...Ronda...costa del sol....Grenada.

If beach time is a must, instead of the Costa del Sol, which is quite overdeveloped, overtouristed, and charmless, I suggest the Costa de la Luz, which is conveniently right next to Cadiz. The Costa de la Luz is where the local Andaluces go for their beach holiday. You can read more here - https://www.spain.info/en/region/costa-la-luz/

PS: Also don't forget Cordoba! My favorite city in Andalucia. Make sure to stay overnight to enjoy the city for yourself after the peskey daytrippers have left back to Sevilla,

PPS: I'd say for the trip you're planning you'll need at least 16 nights minimum.

Costa de la Luz is an excellent recommendation for the "beach" segment. I especially like Zahara de los Atunes: the village itself is a bit ramshackle but the beach is incredible, and there are plenty of excellent restaurants there.
You would need a car in those parts, basically for the whole segment between Cadiz, Ronda and Granada. I am sure you could rent a car in Cadiz and return it in Granada.

For most North Americans flight timing usually makes more sense to fly into Sevilla (probably connecting in Madrid), then work your way north, ending in and flying out of Madrid. (Caveat on the most and usually)

Renting a car is so much more than the cost per day of the car. Add gas, tolls, and parking as additional costs, and add navigation and parking as frustration factors. I'd say transit unless you're really going remote places.

When I'm somewhere for 3+ nights, and per-nights are similar or better, I usually prefer AirBnBs. Apartments can offer some flexibility and cost savings beyond hotels.

My wife and I try to stay at Paradors (government run hotel chain) in Spain when there is one in a town we’ll be visiting. I also agree with the Costa de la Luz having some nice beaches. Ones near where I used to live include Rota, Chipiona, and San Lucar de la Barrameda. Of those, Rota will be busiest from May through early September. It is popular with German tourists. As Carlos stated, if only visiting cities public transportation makes more sense. A rental car comes in handy when visiting very rural areas and sites. While gas, tolls, and parking add to a rental car’s cost, gas and tolls are fairly nominal. Parking in larger cities will add up, but is free in most small towns.

Your trip sounds similar to my plan in early June. We are flying into Madrid from Cincinnati. Seville was not as accessible for us. I feel like it was more $$ and maybe an additional stop? Once we land in Madrid in the AM we are getting on a train for Seville. 3 nights there then renting a car (Enterprise) to see some of the hill towns on the way to Ronda (2 nights). From there drive to Nerja for beach time (2 nights). Then drive to Granada, return car (3 nights). Then train back to Madrid.

I would say do airbnbs. More bang for your buck plus you’ll have plenty of common area for you and your honeymooners to share. More intimate! And if you wanted to hang in for dinner with wine and such, a lot of them have incredible rooftop space.

Hotel Playa de la Luz is wonderful and reasonable!

As an FYI, Hotel Playa de a Luz is just outside of Rota on the road the Chipiona. A nice hotel in Rota itself is Duque de Nájera. Both hotels are right on the bay.