Congrats on getting ready for home ownership! The first thing I will address is a comment made below regarding "part time" income. I have never heard of a lender asking someone what hours they work. Your income is your income, part time, full time, or no time. As long as you have proof that that is what you paid Uncle Sam on...it is your income. It looks as though your credit score is OK also. The only issue I see is the 150K mortgage with $4K down.
FHA requires 3.5% down which would be $5250 not including closing costs (which you could ask for in negotiations)
Do you qualify for a VA loan? (veteran) Then you would be looking at 0% down
With your 30K income the max payment allowed is going to be $750mo respectively. That is based on a 30% front end qualifying ratio.
To get in a $150K mortgage and have a $750 payment you would need aprox. 50% down ($75K) Keep in mind you need to add property insurance, Taxes, and PMI. Total payment would be $777.62. (based on 1.5% property insurance, 3% property tax, and no PMI calculated)
So as you can see You are a ways off despite the comment about being on the cusp of qualifying.
With $4K down you would need to look at a property no more than $85K.
Keep in mind my specs for providing the info
3% property tax (your local rate will differ)
1.5% insurance (typical rule of thumb)
You still need to consider PMI unless you are able to put 20% down.
All this said.....
I recommend sitting down with a lender. They will be able to give you concrete information. Mine is just guideline info. And not 100% accurate (pretty doggon close though)
I hope this helps you!