Don't pay for first class on the TER. It's not worth it. Most of the time (every time?), there's no first class anyway.

As mentioned, you can either exit BSL via the French/German exit and take a bus to Saint-Louis station, or the Swiss exit and take Bus 50 to Basel SBB.

You'll save a few € taking the French option.

(Live in Basel, taken the TER to Strasbourg many times.)