My tuppence worth:

A 3 towards Würzburg/Nuremberg (AKA A3 East) is no good after Aschaffenburg, where it becomes a narrow, 2x2-lane, hilly nightmare, and very prone to congestion.

A 5 North, Frankfurt commuter hell, construction and speed limits. Avoid!! A 5 South is equally horrible.

A 45 north means fog, fog, and more fog (but it's lovely on a fine day).

A 3 north (Cologne) is not bad at all, but as a novice, you'll find that the local big boys are out in force in the fast lane (plus there are some long term roadworks near Limburg - cue serious delays).

My personal favourite is A 63 Mainz-Kaiserslautern (AKA USAF Ramstein). From FRA, follow signs for Wiesbaden/Köln (A 3), then after 2 miles or so follow "Mainz/Bingen" (A 67 and A 63). Once in Mainz (a 15 min drive), follow "Kaiserslautern" on A 63. This Autobahn (a) is new and in very good condition, (b) only has about 10 kms of speed limits, most of which are of the mild 130 kph variety, (c) sees hardly any HGV traffic, and (d) takes you through some beautiful scenery. The best part is a bridge at about the halfway point - a straight slope takes you onto the viaduc across a large valley, meaning you have about 2 miles of dead straight and descending road before you for acceleration. Full throttle - it's marvellous (beware of crosswinds though). Make use of the hill on the other side of the valley before negotiating the bend...
Oh and the US MP patrols part of A 63, but that should not concern you unless you're currently an active US armed forces member.

Once you reach Kaiserslautern, you can return on the A 63 or return via Mannheim (A 6 east - A 67 north - FRA).

Tom