Note that the train systems in Denmark and Sweden are very different:

For SJ long distance trains in Sweden (X2000) you'll definitely want to book in advance to get a decent prize. They start selling the cheapest tickets 90 days before departure and for popular trains they run out quickly. Reservation is included with the ticket, which is bound to a specific train (airline-style). You can NOT just hop on any train.

The regional Öresund trains (Copenhagen-Malmö-Gothenburg/Karlskrona/Kalmar) on the other hand are run by the county transit authorities (not SJ). Tickets are fixed-price and valid for any departure.

For Copenhagen/Malmö-Kalmar you have the choice of either Öresundståg (some find them uncomfortable, I don't) all the way or SJ with a change in Alvesta.