We don't get much mold in our apartment although it's an older
condo (well, old for Singapore - over 30 yeas old). I do get mold on leather shoes though so have to keep an eye on that - they usually just need a polish before wearing if I don't wear them often.
Clothes smell musty after a few months if they're not worn. I used to spend a small fortune on those thirsty hippo things when we first moved here but they didn't work that well so we haven't bothered with them for years. What I do now is just wash the clothes a few days before I want to wear them. If you wear them often it's no problem, but if you have something special and you only wear it for weddings or something you'd need to plan in advance. Likewise I have to wash our warmer clothes before we travel to colder countries as they always smell musty because they only get worn then (vacuum sealed bags never seemed to work that well so I stopped bothering with them)
We always remove shoes before coming into the house which is an easy thing to do here as they're usually sandals or flip-flops and there's a dry place to store them outside the apartment. I don't know what we'll do when we move back to Europe as it's a house with no porch or covered area outside, but I'd like people to continue removing their shoes as they come in because we're in the habit of doing it now. It's harder there though as people wear 'trickier' shoes like boots and things.
More than mold, the main problem we have is things perishing or going rusty. Computer parts stop working due to the climate affecting them, bikes go rusty really quickly, things perish because of the heat/humidity - I had a light fitting in the kitchen fall apart in my hands the other week when I went to change the bulb and we had to go and buy a new one. My trainers have just been binned because despite only being 3 years old they were falling apart (the plastic and rubber parts had started disintegrating!).
You also get mildew on things like books and photos (don't bring valuable books or precious photos here, leave them in storage). Books which were only bought 5 years ago look like they're 50 years old. Also pictures behind glass (especially photos) - they can stick to the glass and you'll never be able to remove them from the frame.
I don't think I'd bother with a dehumidifier - it'd be like fighting a losing battle (and I'd probably forget to empty it!)
Our stuff didn't go moldy in the container on the way out but we're about to move back again - I'll have to see what condition it is in when it arrives. It will probably be too late to let you know though as you sound like you're coming here soon and our stuff won't arrive until August/September I guess.