Has anyone purchased point-to-point train tickets in advance? Which trains to avoid?
 

I've been looking at the country-specific rail websites and finding some good deals if you purchase early and don't change your plans. These would be ideal for me because I have to do a stretch from Lucca to Innsbruck for sure on a certain day and then another stretch from Innsbruck to Mannheim on another day. Any experiences buying tickets ahead of time? Also, which any certain trains I should try to avoid (crowded during certain times, etc)?

You don't make clear whether 'ahead of time' means before you leave home, or after you arrive.

I've gotten deals by buying a few days in advance once I got there, directly at the station wicket. For example, I bought tix from Verona to Innsbruck in Italy at a discount because there was a 'two travelling together' special on.

I've also bought in advance on websites, especially France. The catch of course as you already have discovered is that the best deals are sometimes nonrefundable, so you could be out some money if your plans change. Other tix I have bought simply to have that task over and out of the way - and to be sure of getting a seat (which turned out to be critical on a fast train from Faro, Portugal to Lisbon - that train was packed that day and time.)

It is almost impossible to predict which trains will be crowded. So much depends on local conditions (was there a 24-hour strike the day before or scheduled for the day after your day of travel? A football game going on in your destination city? etc. etc.) Often ticket prices are higher on busier days, reflecting market demand.

>Also, which any certain trains I should try to avoid (crowded during certain times, etc)?

If you have bought a ticket like this it always comes with a seat reservation, so the crowding (or not) is rather less substantial.
Otherwise, avoid the trains that run between major centers on Friday and Sunday afternoons and Monday early mornings (before 9)

Post-trip update:
I purchase tickets online through trenitalia.com. It worked out pretty well and it was VERY cheap to go from Lucca to Innsbruck. The tickets weren't flexible at all, so I don't know what would have happened if we missed the exact train though.

The reason to buy ahead on Italy-Austria Allegro trains is not that the train will be full but you can get a hefty discount at times by nabbing one of the limited discounted tickets that often sell out way in advance of the train

Ditto perhaps for Innsbruck-Mannheim at www.bahn.de but maybe only Munich-Mannheim would offer their SPAR fares on that route