CRZ automatically dumped players from multiple realms into the same zone instance so zones didn't belong to any specific world. You had no choice - the game chose for you.
With World Visit, zone instances will continue to belong to a specific world and you will have to specifically choose to opt in to visit another world's zone instances.
I'm still leery of the potential for cross world trolls to screw with zone activities on other worlds. It could be the trolls will get bored with it fast since moving between worlds is somewhat inconvenient and you're cut off from things that can only be done on your home world.
In the long run, it's likely to only be used to visit and play with friends on other worlds in the same data center. I don't think it will harm FFXIV the way CRZ harmed WoW.
Players will be able to buy from the MB on the worlds they visit. It doesn't sound like we'll be able to direct trade, though. It's an advantage for those who might have problems finding certain rare items on their home worlds. I don't expect it to have any significant impact on the majority of items sold on the MB since most players aren't likely to world visit to make a normal MB purchase.
There is some real concern about how crafting/gathering bots will further impact prices of crafted end game items but we'll have to wait to see. It could be SE has unannounced plans to crack down on those bots as the same time World Visit is implemented (probably a pipe dream but who knows).
Yet this also has the potential to increase buying power of the low pop servers in the long by giving their sellers new customers while buyers have more opportunities to get what they want.
Unless you've been making your gil by monopolizing certain commodities on your home world, there should be nothing to fear.
This is one area where FFXIV isn't copying WoW. There is no cross realm AH in WoW.