However, if I sell my business then do I no longer qualify to buy a property in the future?

They are more than qualified, just don't want to go through the vetting process.  

I'm thinking about selling in the next year and I have read that if I now live in the property for the last 2 of 5 years that I won't pay taxes on the first $250,000.

RE is nothing but math, just know your numbers ,Buy right, reno right, rent/ sell right, YES that simple LOL 

It was intended as a fix and flip, and our original exit strategy was reached. we bought with hard money then did a refi to convential because repairs became drawn out and rented for some cf to by is time. we ended up selling for 405,000 and our loan balance was 235,000.

Since this will be my first time buying out of state, does anyone have any advice or experience with this process?

You should look into DSCR Loans - many investors like yourself typically move to this loan product once they max out with DTI/qualifying conventionally - a bit higher in rate than conventional mortgages - but no DTI ratio or tax returns/income verification makes a much easier qualification process and LLCs are 100% ok (even as sole owner) and actually often preferred.PS - published a 10-part article series here on BP last year on everything you'd want to know on these loan types - sharing links below, hope it can help!

They may be able to transfer title to LLC after closing, but it will be best to check with your lender if there are any restrictions to do so prior to that lender selling that loan in the secondary market. 

We are currently doing this process now in San Diego!

Often not as much as retail centers with lots of property management but still takes work, knowledge, and skill.I have a whole process I have developed to assess risk.Hope it helps