John,
We did the Primitivo last August and are intending to do it again this coming August. Definitely there are cash machines in Grado and Salas - I can't remember exactly where else between Oviedo and Lugo but you pass through enough decently sized places for it not to be a big concern. It's probably a good idea to have enough cash on hand for a couple of days because it's hard to predict exactly where the next machine will be. There isn't much to buy in the isolated stretches beyond a beer and a sandwich so you probably won't need a lot of cash. I think we had about 100 euros each on hand between 3 of us - so total of 300 - and we tried to keep it topped up to that level. If I were alone I'd probably carry 200 (just in case...but it's almost certainly more than you actually will need) and a credit card - but keep in mind that there are some quite isolated stretches. Of course this also depends on how many kilometers a day you intend to cover - I'm basing this on an average of about 25-30 km a day. Overall it seemed like a very safe route and we didn't spend a lot of money overall.
The total accumulated elevation gain between Oviedo and SdeC is about 30,000 feet with a similar total accumulated loss and it's gorgeous!
We had ultralight tents which were really useful because several albergues were full and they were good to have in case of emergency. Make sure you take some warm clothes (layers) and some waterproof clothing and/or a pack cover or poncho. We had 3 straight days of rain, cold and fog in the mountains before the heat of Lugo! We knew that rain was a possibility but were surprised at just how cold and wet it was!
Buen camino
David