Borrowing money. What order should I tackle each of these steps?

[Tim Woosley]

I plan on getting pre-approved for a loan for a multifamily rental purchase. I also want to open a line of credit in case of an emergency (since I don't have a lot of capital yet.) I also would like to refinance my home for a better interest rate. 

I'm trying to strategize on what to do first. That is a lot of hard inquiries on my credit score and I'm trying to be tactful with this. 

I was going to get the handiline first in October and then wait 7 months to get preapproved (since it takes that long to have a hard inquiry removed from your credit history). But then I also thought that it might be a good idea to refinance my current home to save on some interest there before rates go up.

What do you suggest the order should be?