I think you may want to start looking now. Don't be in a huge hurry to buy, but be open to the first house you find that would meet your needs for a reasonable price.
I'm making the following assumptions for my calculations:
* A house of the size, location, and quality you're looking for is currently in the $450k price range, meaning your current 10% down payment savings is worth about $45k.
* You're saving for your down payment in a savings account that pays negligible interest (but also won't go down in value over two years).
* Your current mortgage is a 30-year fixed rate mortgage that you started paying off five years ago. Your monthly payments are in the neighborhood of $1350/month, and you plan to make no more than the required payments on this loan (meaning you'll owe about $246k in two years if you keep paying this mortgage).
* In addition to your mortgage payment, you can afford to save $2,500/month toward your next house. This is based off of your estimate that you could get up to a 20% down payment in 18 months.
If you sold now, you might net $15k on your current house after paying back the bank, realtors, local excise taxes, and other closing costs. Add that to your $45k you already have saved for a down payment and you'll have to borrow about $390k to buy that new $450k house. You're already paying $3,850/month between your current mortgage and your savings for your next house, so why not get a 15-year mortgage at 3.5% instead of a 30-year loan at 4.625%? The required payments on this mortgage are $2,788/month. If you keep putting the full $3,850 toward your house like a good Mustachian, your mortgage balance will be down to about $320k in two years.
What if you wait two years to buy?
Let's suppose you wait two years, and also suppose house prices go up 10% in that time. Your current $300k house will sell for $330k with a remaining mortgage balance of about $246k. Selling then might net you $55k after expenses. You will also have saved up $105k toward a down payment. Your new house will now be worth $495k (up from $450k), but the increased value of your old home coupled with your increased savings by waiting will mean you need to borrow about $335k to buy that house. This is less than the $390k you would borrow if you bought now, but more than the $320k you'll have left on your mortgage in two years if you bought now and continued plowing your savings into your mortgage.
What if house prices go down by 10% instead? Your current house will be worth $270k with a remaining mortgage balance of $246k. You'll probably net less than $5k from that sale. I'll assume you just break even. Your new house will now be worth $405k. Your $105k savings means you'll have to borrow $300k to buy the new house.
If you wait and prices go up, you'll have a higher mortgage balance in two years compared to if you bought right now. If you wait and prices go down, you'll have a lower mortgage balance compared to if you bought right now. However, pretty much nobody expects interest rates to be as low in two years as they are now. If you wait and prices go up, you'll borrow more and pay more interest per dollar borrowed. This would not be ideal. If you wait and prices go down, you'll borrow less but you may still find yourself paying just as much interest (or more!) over the life of your loan, and you'll face the additional risk of finding it harder to sell your current house.
Given all that, I would say your best option financially would probably be to buy soon to lock in today's interest rates. I think the risk of higher interest rates in the future dominates any risk from price fluctuations.