First deal overthinking all details - Points and Closing Costs

[Michael Litle]

I'm about to offer on my first deal, a duplex in a slightly expensive market but will cashflow fairly easily.  I found a lender through BP who seems very knowledgeable, experienced, and likely someone I could grow but before I lock everything in, I can't help but wonder if I'm wasting valuable liquidity early on by paying $12k in closing ($7500 for 2 points).  Should I be nitpicking closing costs?

The deal breakdown will be likely a $420k offer with 10% down @ ~6%.  With Closing costs, mortgage is just over $2500 and rent for both sides is $3200 - $3500.  Overall an excellent first deal I believe, but I'm already ready to find make my next offer so I don't want to chew up cash I might need on the next down payment.

Am I over analyzing while I'm trying to learn this process?