okay, keeping to your budget is important to you, so get a magnet mount antenna as you already have a rubber duck antenna that came with the scanner. While neither may be specifically tuned to RR frequencies, which would be best, they'll work.
Your particular hobby is an interesting one and perhaps someone with the same interest will chime in on the transmit power and antennas used by the RR. It appears your interest is to hear the chatter and spot the train. If their signals are strong, you may hear them with plenty of time to get to a crossing.
I have a $15 wideband magnet mount antenna that beats the pants off that Diamond 77CA because it's on the roof of the car. You could use the mag mount indoors as well, but put it on the top of the fridge or an oven pan so it has some sort of base as a radial. Experiment with it in different spots, but that is a reasonable solution you can use at home or in the car. Prcguy provided good advice about a tuned antenna, but if you are uncomfortable with that, get the Diamond mag mount and have fun.