On driving - I would only drive if you want to head right out into the country - the Atlas or the Sahara, for example (but for the latter, I'd park at the edge and get one of the desert buses on to a town like Merzouga). Otherwise, ONCF operate an excellent train service from the Algerian border all the way down to Marrakech via Fes, Meknes, Rabat and Casablanca. The big gap is Essaouria, but it's easy enough to charter a grand taxi for a group of you.
I'd recommend 2nd class over 1st class on the trains too - particularly if you speak a bit of French or Arabic, as it's incredibly sociable, and so a great way to travel.
I'd strongly recommend Meknes - it's like a relaxed version of Fes, and has the remarkable ruins at Volubilis close by. Rabat has a beautiful, whitewashed Mediterranean medina, and while Casablanca isn't that fascinating in itself, the Hassan II mosque is a fantastic building, and one of the few mosques non-muslims are allowed to visit in the country.
However, by hiring a car, you can head down through the mountains from Fes through Midelt - a great place if you're interested in buying a carpet, as it's home to many independent and co-operative weavers. From there, you can head to the edge of the desert, and get over to Merzouga, a good starting point for trips out to the dunes - particularly on small camel safaris. From there, it's a long, winding road down to Marrakech via Ouarzazate, via the amazing gorges around Tinghir.
Driving that road, though, is not a relaxing experience - at least, it wasn't when I did it (about 10 years ago now). A winding road, with only just enough room to get past a truck (and there were plenty of them heading towards you in the middle of the road), sheer drops with no protective barriers and, perhaps worst of all, quartz salesmen leaping out into the road to try and get you to stop. Plus, if you're not used to manual transmission...
Anyway, it's a fantastic country, and any trip to Fes, Meknes or Marrakech is going to be thoroughly enjoyable. Do relax, and do always deal with touts with a smile and a sense of humour.
Redhead - I can't offer you specific advice on being a female travelling along, but I know that things have improved in recent years due to the establishment of a tourist police force. Touts are everywhere, but far less persistent than before. As always, engaging, becoming flustered or irritated are the worst things you can do: if you let them know they're wasting their time, with a mix of humour, feigned ignorance and haughty disdain, then they'll be off to a more obvious target in no time.