It sounds like OP is traveling from outside the US. If you arrive in Chicago, the transfer from ORD to Union Station (Amtrak) is a trial -- very difficult by public transport. Best to fly up to Rochester or even La Crosse itself (on AA or DL, not UA). If you can arrange to arrive in Minneapolis (via DL most likely), it's easiest to forget about the connecting flight to La Crosse, hire a car at MSP, and drive. Pretty countryside, less than three hours.