"Last time I hiked to kjerag in norway with a 12 euro pair of runners. It was fine, but I also only brought a backpack with a jumper, water bottle and camera.
The area I want to go to might be a bit more wetter, and harsher terrain."
If cheap shoes worked before, why go heavyweight now? If it's wet, and you want dry feet, wear gaiters or waterproof socks. But a guide I hired in Yakushima - which gets up to 12 METRES of rain a year, used to wear really cheap runners. I asked him about wet feet and he just shrugged - who cares?
The Backpacker/REI thing about "weekend boots" and "5 day boots" is frankly nonsense. So long as you have rock plates in your runners, boots aren't going to be any better in harsh terrain.
"I was just considering the boots because I've had a few bad sprains and my ankles aren't that strong, especially with a backpack on."
This is a pretty common rationale for boots - but if you have bad ankles, even surgical braces won't help - I used to play rugby with a guy who would lace on a plastic surgical brace before every game, but even that didn't work. If that doesn't work, boots certainly won't - remember that even the stiffest boots have to flex along your shins and at the ankle, or you won't be able to walk. Exercises, orthotics and surgery are the options, in order of how bad your ankles actually are.