It'll tell you a $500k conventional mortgage was recorded in July 2021, you can infer from the ownership record that it was a refi (same owner before/after), and you can ballpark that rates were around 3%, assume it's a 30YF, so the balance "should" be X, but you have no way to know if they made a large lump sum payment, pay extra each month, etc. 

We are choosing new build because A) our family 4 has a certain size demand B)  the price-quality ratio doesn't seem to make sense when considering a preexisting home C) with interest rates being at near 8% with preexisting homes, builders are offering 5.99% interest rates and the exact home we are looking at is about $75K discounted because it's a spec home and the builder doesn't want to pay taxes on it.So, live in it for 5-6 years hopefully rent it out with a fully finished basement for potentially $4,200 in 5-6 years.

My mortgage payments are currently $2,841.40/month and my property management fees are 4% (I'm striking a deal with a property manager I trust so I'm super thankful for them giving me such a low rate).

Not a "hey let's read everything" journey, no, pick a strategy, get THAT highly rated "how-to" book. 

What loan type (DSCR or conv) should I be looking at and what rates?.

It really depends on your investment goals.

Each way you're making money on the property, it just depends upon the type of use you can envision.

This will be done as a "rate/term" transaction, so better rates than a cashout transaction. 

I pay in the area of $240 per month, but that will differ depending on the property.

In the 80s interest rates used to be double of what they are today and people still succeeded.