It's probably a good idea to start low with your first investment property and the market is still favorable for investors........there are always good deals, it is just a matter of knowing what to expect, the market trends, and if the rental market is strong in your location of choice. There are areas of Walnut Creek where the rents are quite strong and yes, you could still purchase in a nice Walnut Creek neighborhood and stay in your budget of under 200,000.
Antioch will have a BART extension pretty soon. Even though prices have gone up, it is still possible to find single family homes < 200k in Antioch. Are you planning to get a loan ?
Alternatively, you can get a heloc on your primary and then buy the property cash.
Best of luck.