Option #1, selling your home in Oregon and renting in Arizona for awhile will give you the most buying power because "Cash is King." I've been able to negotiate some very good prices by offering all cash, 30 day escrow, i.e. no complications from the seller's perspective. Renting for a few months before you make an offer on anything will allow you to be sure it will be the house you want in the neighborhood you want, and if you are a month-to-month tenant you can rent past close of escrow to give you time to make any improvements before you move in to your new home. Yes, you will have to move from Oregon to Arizona and then move again across town, but you are making a life changing decision when you relocate to a new region so the extra time to maximize your knowledge of the current conditions of the local market will be worth the inconvenience.
Option #2, making an offer contingent on the sale of your existing home, is a common practice but complicates the deal for the seller. You wont have the same bargaining power as with all cash or "cash to new loan." You also run the risk that it will take too long to sell your existing home or that you won't net enough for it, in which case most contracts with that contingency give the seller the right to cancel the contract if the buyer cannot meet a relatively short deadline. Be very careful about the language relating to return of deposits. If you go this route be sure that you get all of your money back and are not penalized if you cannot sell your home in time. The silver lining here is that assuming you get all of your deposit back, you really aren't worse off than had you chosen Option #1 to begin with. The only bad thing that will have occurred is that you lost out on a house you liked and wasted a bit of time and effort.
Here is what I negotiated on a house deal that opened escrow yesterday: Large down, relatively short escrow, seller to carry remaining balance to allow me to sell my current house in the spring/summer when the market is better without the sale of my house being a contingency for the purchase the new house. This will allow the seller to use my down payment to purchase a small retirement home on the other side of the country where he and his wife have been renting. Since Seller has no immediate need for the remaining balance and it would likely sit in a money market fund for a while anyway, at a fairly low yield, he is getting a slightly better return on his capital by lending it to me on a short term note. This also gives me the option of borrowing against the equity in my current home rather than selling it in order to pay off Seller's note on the new home, and then convert my current home into a rental. This arrangement also allows me to take possession of the new house before I have to do anything with my current house so I can remodel the master bath before I move in. Win-Win.
BTW, this will be my new yard and "water feature":
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