Among your three choices, I would recommend the Sta Fe, even in the current gen, it is a performer.
Maintenance wise, I'm surprised to hear you say the Fortuner would be more expensive to maintain? If it is a diesel, it should more or less be the same. And if it is a korean car, replacing the battery would most likely mean replacing it with a Korean battery.
Before in our Old Carens, we needed to change the battery and since it was a brand not sold locally except through the dealer, we purchased it through Kia. It was a shocking sticker price of 10,000php for the battery.
I understand you can get a local equivalent battery for this but as was advised by technical persons, if you want to prolong your alternator, you stick with the same brand and model of the battery so the rate of discharge is the same throughout its life.
I am not sure if the current Sta Fe and Sorento uses already a locally sourced battery so that is something to consider as well.
You will have a cheaper maintenance regiment if you use a gasoline fed engine compared to a diesel. This is just for info.
If you are comparing the Fortuner to the Sta Fe, then you would just spend a bit more for the synthetic engine oil of the Fortuner because it is 2.5 as opposed to the Sta Fe 2.2.
As for resale value, if you really plan to keep for a long time (beyond 5 years) then the difference is negligible.
Based on my experience, the Koreans have 2 major quirks that you may experience within the 3 year period. That is a suspension problem (tatagtag kaagad at kelangan palitan) and also a turbo problem (will need replacement if it is your regular vehicle). If these two would be the problem, they usually take around 3 weeks minimum to have the part ready. Both are covered by warranty though.
Have friend whose Sta Fe had a repeated Stereo problem because it is no longer an OEM part from Hyundai once it is sold here in our shores. It is already an aftermarket part from Winterpine. It's a case to case basis for the entertainment unit though so it is not always the case.
Hope this at least helps in additional info for you.
But among your choices, I would really love the Sta Fe. Check more with other owners on their take on after sales service performance because it is the biggest question mark I had that could not be clearly answered when we decided to purchase a diesel SUV. Too many factors were at play already so steered away from Korean cars already. But that's just us last year.
Sta Fe is also clearly very fuel efficient if that is one of your considerations. =)