How to negotiate

750 credit score, ~$32K saved for down payment. What's my next step to buy a house and how do I "shop for a mortgage"?

Get a conference line and get Citi-Chase- Wellsfargo to get on a call to pitch u their best package. You may need to complete a preapproval app.Soft credit check Worked for me Citi paid our closing cost with a Lifetime servicer loan 30yr fixed $230k 3%

This sounds like a crazy, yet awesome idea. How did you do this? Was it a surprise for the banks? Did you agree to go with one of them on the spot? 

Yea Mortgage brokers only earn commission no salary, so they are really incentivized to "close you",if you have strong application ( High Credit score, Decent job {2+yrs}, CASH down $20K>{skipping mortgage insurance} and If you are a 1st time homebuyer) than they want u bad so make em work. I had 2 pre-approvals (MCU,Citibank) so already had a relationship with both brokers and for safety I got WF and Chase on the line, all spoke to prior hand- And they will def be shocked, everyone just chuckled once they realized they were on conference line But I just said " Ok guys thank you so much, as per our discussion, you are all aware of my app package and my offer is accepted and i have already put a deposit down with the moving company so now get me a mortgage- MCU offered $1500 towards closing- Chase gave me 45day guarantee to close and WF offered me points and CITI paused came back and said " we can offer the same rate as these guys + we will pay your closing cost". I asked can anyone match or beat that, LONG PAUSE- Thank you Got the CITI Processor to add my personal lawyer fee to the closing docs(HUD) and at the closing citi just handed out $ to everybody. Personal note our attorney was shocked as to why the bank was paying him but just ease that fear and say shush you will get your money :) 

How much should I have saved to buy a house? Down payment, closing costs, anything else that comes with it? 

I've written this before, but the biggest financial mistake of my 20's was putting too little down on the down-payment and having PMI. Flushed a few grand down the drain when the ex and I could have easily covered the 20%. Evidently, we preferred to have it in a savings account to stare at it...I did recognize the mistake and paid down the mortgage aggressively and then worked to erase the PMI, but it was a silly mistake.