I agree with Boger here: thinking about these sorts of things now and planning ahead is the right thing to do when dealing with long-lived animals such as reptiles. This is particularly true if you're just starting out and thinking of how (or if) you'd like to expand your menagerie.
From personal experience, I'd say you might be pleasantly surprised how some landlords are viewing pet snakes nowadays. Once they learn they live in a box, don't free-roam the house, and don't make a stink, they're typically happy to let you keep them. Bonus points if they see door locks and safety regulators like Herpstats.
Things are definitely different on the avian and large scale aquatics front. Small birds are typically tolerated, but large birds such as parrots may be a no-go. Most apartment buildings also wouldn't allow a tank such as your 125 gallon -- most only allow tanks up to 30 gallons or so. It's also incredibly annoying to move a tank any larger than that, so I wouldn't recommend keeping a tank that large going if you think you'll be moving around a lot. There's a reason why I've only kept betta fish for the past few years.
In addition to thinking about landlords, don't forget to think about exotic ownership laws in the places you may move. More than a few towns have "no snakes over six feet" rules, and more and more states are starting to place restrictions on native species possession as a result of rampant poaching. For example: I've been seriously thinking of getting a cornsnake as of late, so I've done a little forward research into native reptile ownership laws in the states I may move to in the future. Many states restrict the ownership of wild-type and dark-eyed corns while allowing albinos/amels to be kept at-large. So, as long as the corn in question is an amel or amel combo, I'd be okay.
Long story short: it's good to plan for the future, but don't overly fret about it. You probably won't be forced to live animal-less, but you will probably face some constraints in terms of the types of animals you can keep.
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