Speed Control
Do some speed control drills to ready you for straight pool. While obviously speed control is important in all games it is different for straight pool compared to your usual games in that 14.1 is played much more often with a softer stroke at lower speeds in congested traffic. In straight pool you more often must hit a spot with your cue ball position rather than an area because the proper position on the correct next shot requires you to shoot between two other balls. Missing position by even a hair and that next shot will be obstructed.
The "L" drill is good. So is the the drill where you place the CB in the center of the table and all 15 balls in a circle around it. The object is to run as many as you can without going to a rail.
Practice shots into the corners at the foot end where you are jacked up and have to bridge over a ball (happens often in straight pool). Practice these with English as well. This will improve tip placement control.
Another good shot to practice for straight pool is the down corner shot with both the cue ball and object ball somewhere behind the footstring, practice making these shots into one of the corners down table at the head end. Practice these shots at different angles These shots can come in real handy to keep a run going and you don't encounter it nearly as much in say, 9 ball.
You will encounter combinations, caroms, and rail first shots more in 14.1, so practice these.
In terms of the thought processes in straight pool, try setting up some angle shots into the two foot end corners with both the CB and OB balls at the foot end of the table (do some of these from behind the rack). Place a cluster of 3-4 balls in the natural areas the CB will travel after hitting the OB. Prior to hitting the shot try to visualize in advance what will happen to the cluster and plan shape for a shot on one of those balls. See how it works out, and try it again.
In straight pool as opposed to 9 ball especially, the idea is often to plan position for more than one ball on a lot of shots. This thought process can help keep a run going that would otherwise end. Try doing this when simply practicing running balls. Plan position on two balls on every shot. This increases your flexibility and can give you extra outs when one of the positions doesn't work out.
Also incorporate into your thought process the idea of thinking more than one ball ahead, even to the end of the rack. Every time you come to the table in 14.1 identify your best break ball and the key ball that you will sink just before that to best obtain shape for the break shot.
Hope this helps.