From Arezzo, you will most definitely want to look at the bus options. The buses are located across the street from the train station. The trip takes about an hour and a half and it will leave you just a bit outside of the city center at Porto Ovile. It doesn't leave from the same place, so make a note to find out where it starts from (it may still do a pick up at the same place, just ask the driver) Be sure to always check the times, it is not frequent and you don't want to be left behind. Remember Sunday always has different hours than the rest of the week. Tickets can be bought at the train station.
As for Modena, pick your trains well. There is an Intercity which costs a bit more but it has no changes and will take you directly to Modena. Expect about a 2 and a half hour trip. The IC (intercity) train is not as frequent, but it is definitely the easiest of your choices. I love traveling by train, and though there can be delays, personally I have never had any troubles (5 - 10 minutes is nothing as long as you are not counting on making connecting trains)