You posted this in Rick Steves Tours, so I'm guessing you are somewhat open to that option.
Here's the link to the Best of Scandinavia in 14 Days tour. It looks like there are many July dates still available. I took this tour in 2018. It's well worth the money. Click on the Itinerary and keep in mind that there is much more to it than the things highlighted in the short daily descriptions.
You could add a side trip before or after to Finland. Or maybe do the Best of St. Petersburg, Talinn & Helsinki in 9 Days before or after.
If this is your first trip to Europe, it would be good to thoroughly explore all the sections of the Travel Tips on this website.
For details on the Scandinavian countries, go to Explore Europe and click on your country of choice. This is a very useful starting place for helping to plan the trip by yourself. Having self-planned all of my trips before 2014 I can definitely say that I learned much more on my RS tours than if I'd planned a similar itinerary on my own. And we went places that I'd never have even thought of on my own.
The bad thing about going to Scandinavia is that all the currencies are different. The good thing is that cash is rarely used. Almost all transactions, even the smallest, are done by credit card.
Most seasoned travelers will tell you that Eurail is probably not the best option wherever you want to go. From the Man in Seat 61, these are the train resources for your countries:
•Denmark - www.dsb.dk
•Sweden -www.sj.se - you can also use •Omio.com (formerly GoEuro.com), www.snalltaget.se or www.bokatag.se
•Norway - www.nsb.no (see advice on using this system)
•Finland - www.vr.fi
All are covered by DB Bahn, but you have to go to the specific country's train service to make your reservations. You will need to fly or take a ferry between Finland and any of the others. DB Bahn covers Finland itself.