It definitely depends on your credit. Both of the new loans will count as a hard inquiry on your score, which will cause it to dip for a few months. If your score is near the limit of what your mortgage lender requires, you may want to purchase the home first.
Talk to your lender before doing anything so she can run some numbers for you. IMO, you should finalize the home loan first. A better Credit Score will get you a better interest rate, which means more savings over 15-30 years. It’s easier to deal with a slightly higher rate on a loan that is lower in principle and shorter.
