Since the biggest risk in the BRRR method is appraising a rehab, it makes sense to find a job that does just that.

As a new investor, what is a good company to use for private lending methods?

Look, we have experience with the methods that were listed in the OP. 

The method I've been using is looking for new construction, specifically of grocery stores (Follow the Walmarts haha) or housing developments.

Needing to and seeing the economic benefit to doing so, are two different things here and while comps in your area are basically apartments and one other SFR, you're 'marketing' for quality renters, a little higher monthly rental yield and should you choose to cash out refinance (BRRRR)- your appraised value. 

Hard to say without knowing how much rehab is needed but as a general rule of thumb: If ARV is lower than 250k: 55% ARV minus repairs If ARV is higher than 250k: 70% ARV minus repairsOf course this method may vary depending of the market but it’s a start ;) Good luck !

And if you sell for $300K and buy fo $300K but keep $50K cash boot you pay tax on that difference.Use this method and your potential liability is pretty clear - It's the difference between the amount you sold and purchased. 

What we've done so far is purchase bandit signs (old school method) and plan to put those out this weekend.

What funding method besides traditional mortgage makes since when buying a rental that needs improvement but there are no comps and the values haven’t been increasing much.

I created spreadsheets to analyze all types of costs and methods of ownership and comparison tables... and I actually joined this community to learn how to use REI to help fund my aviation dreams.