Use bahn.de (4.50€ per journey) or tickets.oebb.at (3€ per train) for optional reservations in Germany, Austria and other countries. There is a seating map on bahn.de
I’ll have a look at your journey. I wouldn’t take the 15:28 train though, it’ll be very crowded as it is coming from Amsterdam + it is often heavily delayed.
Here is the connection I’d take :
- ICE Köln Hbf - Basel Bad Bf 15:14 - 18:49 3€ optional reservation on tickets.oebb.at (add Eurail as a discount and select one-way tickets). You’re not required to book anything, there is about 250 seats left so you could simply sit in any unreserved seat
- You’ll surely arrive at Basel Bad Bf quite delayed
- S6 Basel Bad Bf - Basel SBB 19:19 - 19:25 or ICE 18:48 - 18:55 if it is a bit delayed
- Basel SBB - Bern 19:28 - 20:26