A fantastic day out - if the weather is better than today.
First, you do know the road has it's very own multilingual website? https://www.grossglockner.at/gg/en/index
Departure time: Give the city workers time to get in, set off 08:30-09:00. Depends where you are staying, Salzburg city traffic can get itself into horrendous gridlock at times. For most districts I'd get the B150 south to the A10 autobahn south of the zoo then on that until the B311 near Bischofshofen, west to Bruck and then the fun really starts. Don't forget Austrian autobahns are toll roads, the car needs a sticker, rentals should have one.
The Grossglockner road also has a hefty toll, this is paid before the serious climbing begins, you ought to be at the start within 100 minutes of leaving Salzburg. The main site on the road is Franz-Josefs-Höhe which is actually at the end of a side road. It has a large underground parking lot (free) and other facilities.
There is a choice of cable cars http://www.gross-glockner.at/en/summer/tickets-passes/grossglockner-panoramabahn parking areas tend to be rough flat sites, I'm not sure about costs, they may be free in summer (they are really for the ski season).
Both the websites have webcams, this is important because the weather can be very different to what it is in the city, low cloud may cover Salzburg but the road and summit could be above it in sunshine. Check them out at breakfast time.
Alternative return route is simple, if not faster. Carry on a little further south to Lienz (which is definaetly not the same place as Linz). From here head north west on the B108 Felbertauern road http://www.felbertauernstrasse.at/en/ (with another webcam). If you plan on using this route you can save money by buying a Rundfahrt ticket at the Grossglockner toll booth, this gives you one trip on each road at a slight discount to the total of the 2 prices. At Mittersill head east on B168. This takes you almost back to Bruck. You can return to Salzburg on the A10 or turn north on B311 via Zell and Saalfelden to Lofer then B178 which should be signposted for Salzburg. But before you get there you pass through a corner of Germany (normally no border controls and most of the cars on the road will have Austrian plates). This road is the B21 in Germany and re-enters Austria near Salzburg airport. The trick here is not to arrive too early, traffic is once again chaos in the evening rush hour. Allow 3 hours Lienz-Lofer-Salzburg.