Just looking for insight...

Looking for insight before we go for pre approval. So many different opinions and calculators on the internet, just looking for some advice from a human.

 My partner and I make combined income between 120k-130k. Full time, they have been at their job for over 10yrs. I just switched jobs but in same field. We are both first time homebuyers in NY. I have about 25,000 saved in mutual funds for a down payment. And i save regularly from each paycheck. About 2000 in my savings account. 
 Debt comes from auto loans and student loans. Auto debt totals about 1400 per month (over estimating). Student loan debt just comes from me, totals about 36,000 and I am in the grace period. 

Other expenses (utilities, subscriptions, groceries, pets, car insurance, etc) I estimated about 1500-1800 a month. Probably overestimating but want to be on the safe side. We plan to split 50/50. My credit score is around 680-690. Theirs is on the lower end around 620-630.

What is it looking like we may qualify for? What are our best options? Is it better to wait it out and get better credit?

Every home around us is 350k plus. Less than that is a total shack or gut job.