Your closing costs are going to depend on a lot of factors: price of home, size of mortgage, kind of mortgage, how your contract splits costs between buyer and seller, how much earnest money you put down, day of the month you close on (affects the interest), and maybe some other things. Probably the most accurate way to estimate would be to sit down with your (or a) real estate agent and go line by line through a HUD-1 / settlement statement and add it all up.
You can make a decent guess on the mortgage payment. You can get the PI part by figuring out the mortgage size, length, and interest rate and putting that in any mortgage calculator. Mortgage size will be essentially purchase price minus down payment. You'll also have TI (taxes and insurance) which you can guestimate by looking at the existing property tax rates and the value of the home. Insurance you can call your insurance agent - it'll depend on the specific location and characteristics of the home.
The other thing to try to guess at is how the home will impact other expenses. Living in CA, if you're single, you might be able to deduct enough mortgage interest, taxes, charity, and other stuff to be able to itemize, which might reduce your income tax bill. Commuting expenses might change if you're moving closer to or further from your job.
In the end it will be a big guess. You might end up with 4 months savings or 8 months savings instead of the 6 you're targeting. If so, just adjust as soon as you can after buying.
