I'm not from NE so I don't know what is cheap compared to CA but that's great you already you and your wife are planning. If I were you contact a trusted loan officer in your area and have them pre-qualify you. There is no obligation to use them at all but more importantly you can get a better understanding of what to expect as far as down payment, monthly payment, bank reserves etc. If you are not ready right now they will point you in the right direction on where you need to be when the time is right so you can budget correctly.
No, not at all. You might want to look into a home warranty since you have a rental. Out here in the Bay Area it can cost around $300-$500 per year depending on if the property has a A/C, pool, etc. But say you have a plumbing issue as you did all you have to do is pay a deductible which can range from $50-$100 and the rest is covered by your warranty. Another example is any appliances like fridge, dishwasher, microwave, washer, dryer any problems you just pay the deductible and the rest is covered. Fidelity is a good home warranty company that we use if you are interested in finding out more info regarding home warranties.