If a few $ either way are of secondary importance I would say to book your trains now. Pre-purchased tickets will always come with seat reservations (where applicable). I fall in the camp of The Man in Seat 61 that either method is good, but if I have to be on one side of the fence or the other then for you that is how I jump.
Berlin to Prague- you have the choice of-
0615 arrive 1027
0716 arrive 1124
0916 arrive 1324
On any of the above if you went for Eurail you would also have to make a seat reservation for 5.20 Euro each here- https://int.bahn.de/en/offers/seat-reservation
Prague to Vienna-
0615 arrive 1021
0644 arrive 1049
0844 arrive 1249
The latter two are not compulsory reservations, so with Eurail you could choose to just get on, but you make a reservation on the Czech website for 78CZK each (US$3.37)- choose reservation only in the buying process then select your seats off a plan
Vienna to Salzburg- so many trains that is a free choice, no compulsory reservations, but if you wanted to with Eurail see https://www.oebb.at/en/reiseplanung-services/vor-ihrer-reise/reservierung-sitzplatz for 3Euro each
Salzburg to Bern- You will have to change once, at Zurich
0556 Zurich 1120/1132 Bern a 1228
0756 Zurich 1320/1332 Bern a 1428
and every two hours.
The Swiss domestic trains have no reserved seats, and if you miss your connection at Zurich just join the next one. To reserve a seat from Salzburg to Zurich, if you wanted to then do so with OeBB per Vienna to Salzburg as above.