Have you made any accommodation arrangements yet? It's not impossible this late in your travel planning, but you may be limited once you travel north of the Forth-Clyde Valley (Strathclyde). Scotland has become a major tourist destination, a lot of it having to do with "Outlander." It's also a major destination for visitors from North America as it's a beautiful and safe country, and there's not much of a language barrier (generally!).
First of all, if it's your first time over, you'll be driving on the left side of the road, and shifting gears with your left hand. If you're uncomfortable with concentrating on two things at the same time, you may want to upgrade to an automatic transmission. About 80% of the cars rented in Scotland have a five or six speed manual transmission.
There is an incredible amount of things to see and do in Scotland. As you're starting out in Stirling, you may want to visit the castle and the Wallace Monument. The castle is on a hill above the valley below, and the views are amazing. The castle's not bad, either. If you want a taste of modern Scotland, have a walk down the main shopping Street (Barnton Street) and take a quick trip through the Thistles (Stirling's mall).
As Pitlochry is on your list, you can take the A9 out of Stirling, and follow it north around Perth to Pitlochry. The A9 is well signposted. Pitlochry is a charming little town, and shouldn't be too crowded in early May. While you're around Pitlochry, check out the Pass of Killiecrankie, famous in song and history.
Stay on the A9 after you leave Pitlochry. You'll travel through Aviemore, which is well worth a stop, and then on to Inverness. You'll probably want to spend a couple of days there. There are lots of day trips that you can make from Inverness, or you can just hang out in the city. If you are really ambitious, you could try the North Coast 500, which is a driving trip around the west, north, and east coasts, through some of the most breathtaking scenery in the world. It's just a little over 500 miles, which is how it got its name. Check out the website.
Once you leave Inverness, you have several ways to get to Skye. They are: 1) A82 south to Invermoriston, A887 west to the A87, and the A87 to Skye, crossing the Skye Bridge; or 2) A9 north to the A835 at Tore, the A835 to Garve, where you'll turn left on to the A832 to Achnasheen, then the A890 to the A87. Both of these routes will take you to the Skye Bridge. On either route, you can check out Eilean Donan Castle, which is on the A87, near where it intersects with the A890.
There is lots of hiking on Skye. Some of it is easy, and some strenuous. I can make recommendations, if you're interested. The fact that you'll have a car will make a big difference in getting to and from the various hikes. Portree is a great little town, with a beautiful harbour. Broadford isn't so bad, either, although most of the guidebooks give it a pass. The Cafe Sia in Broadford is a great little restaurant. It's next to the post office. Try their Highland Melt.
To get back from Skye, and to avoid backtracking, take the A851, just east of Broadford. That will take you to the ferry pier at Armadale, where you can take the CalMac ferry to Mallaig. Once you arrive in Mallaig, you can spend some time exploring the village before getting on the A830 to Fort William.
Once you reach Fort William, you have lots of choices. You can head south to Oban, or you can take the A82 through Glencoe, which is a popular tourist destination, and then down the A82 along the west bank of Loch Lomond and on in to Glasgow.