Yeah man, it's always exciting to want to make a big move and investment in your life, but we must be ruled by the numbers and not our emotions if we're to FIRE super early! I'm sure other opportunities will pop up in the future, and let me again plug the flexibility of renting... once you buy a house, you're tied, in some degree, to the area. Now, if you or your wife get an awesome job across the country, it's about a dozen times easier to go after it if you want. So don't be sad :) I rent myself for these reasons and others!
As far as your landlord increasing rent, you could avoid that by being an awesome and hassle-free tenant, and also by trying to get him to agree to a multi-year lease... maybe 1-2% increases per year to keep up with inflation, and you retain the ability to leave, but no other rent increases and no booting you out in order to increase rent for a new tenant. You can sell this by saying that you love your place and want to stay but your wife is worried about increasing costs... make his enemy someone else so that you can sell the deal better. It can work very effectively in negotiation!
As for the 1 and 2% rules, they're basically rules of thumb that are highly, highly regarded by real estate investors from here to BiggerPockets.com and beyond.
Long story short, rent on a prospective rental property should be at minimum 2% of value, per month. So a property that's worth $100k must rent out for at least $2,000 a month. If you think that kind of property is hard to find, you'd be very right in this market, as everyone's trying to snatch up real estate and it's a huge seller's market. It can still be done with distressed properties or multi-unit properties, but with single family houses, the 1% rule is pretty much the floor... If you buy a $200k house, it should be rentable for $2k a month. This can still be done and if it cannot, it makes sense to sell or not buy.
Dangers of failing to abide by the 1% rule result in underperforming assets (if you take the risk of running a business, which a rental property is, you MUST demand more returns than the stock market for your time and trouble and risk) or potentially cashflow negative property, in which case you're just speculating on value. Some can do that well, but many who attempt fail at their own peril.
Real MMM's run-in with it here:
https://www.mrmoneymustache.com/2011/10/10/lets-buy-a-foreclosure-episode-2-what-is-the-50-2-rule/I'm curious, in your current neighborhood, what is the purchase price of a house that can be rented for about $3.5k-4k range? And what do you think this prospective property could be rented for?