I would agree with those who say don’t look at a flight to Regina as a way to save money - neither Regina nor Saskatoon are airport hubs - Winnipeg and Calgary are. The cost to fly to Regina is usually about the same as the cost to fly to Saskatoon.
I’d also agree that once you hit land, whether Toronto, Calgary or Winnipeg, best bet for flying is to to switch to WestJet. It’s generally cheaper than Air Canada, as it’s a discount. The drawback to that is that it can have some pretty up-and-down flight plans on long flights, but a flight from Calgary or Winnipeg to Saskatoon would likely be direct (or it may touch down briefly at Regina).
I’ve done the drive north of Superior a few times, and also the train trip. They’re fun, but I don’t think I saved any money on them. (One drive I did, but that was because there were two of us to share the costs.) I’d highly recommend either option to see Canada (about a third of it, east-to west), but I doubt that you’ll save much money. I think air travel is still the most cost-effective for individual long-haul travelling.
The reason for high air fares, even under de-regulation of air travel, is that we have a small population with a huge country. Our population density is the lowest in the G7. We’re the second largest country in the world, with roughly a tenth the population of the U.S. We don’t get many economies of scale in our travel.
For instance, Regina to Saskatoon are about 275 km apart. There’s a good, divided highway between them, with a posted rate of 110 km. And there’s no other major centre on that highway - I think the largest town between them would be Davidson, at about 1200 souls. I’ve done that drive many times, since I appear in court in Saskatoon as well as Regina, plus teaching at the university - and it means a day out of your schedule.
For the OP, get used to the idea that if you want to travel from Saskatoon to any other major centre, it will take a lot of time. However, if you want scenery, fishing, swimming, hiking, canoeing - that’s all just a short drive away from the city centre of Saskatoon. And if you really want to see wilderness, make sure you take a day or two and go north - up to La Ronge or Waskiseu or Meadow Lake.
As for weather in Saskatoon in the summer - congrats! Saskatchewan is beautiful in the summer. It gets hot, but it’s a dry heat, that normally cools down at night. If you’re outdoors a lot, you’ll need heavy duty sunscreen - I typically use SPF 30 (or whatever the rating is to absolutely block UV), because I’ve got a fair complexion. You’ll also need bug spray with DEET, because of the mosquitos. They used to be just a nuisance, but West Nile has cropped up in Saskatchewan, so it’s now recommended as a health measure as well. In a normal year they’re not too bad, but if you’re doing practical vet work, I assume you’ll be around the farm animals. (I drove past the U. of S. campus just the other day, and was amused, as always, by the cows in the field in the middle of town. The U of S campus is one of the largest in North America, because of all the agricultural land that is included in it, although not all of it is in the city of Saskatoon proper.)
All in all, I hope you have a great time in Saskatoon, and that even with your rigourous studies (the vet school had the rep when I was at U. of S. of being the most difficult program, beating out meds), you’ll find some time to enjoy our beautiful province.
Here’s Wikipedia on 
If you do do a roadtrip, this may come in handy: 
