All 3 of my 4-families are at 30-year fixed conventional rates: from 4.5% to 4.875%. 

If you look at rates only, conventional will be best and should always be used if possible.

We are doing a conventional loan at 5% down to purchase the property.My question is, after fixing up and renting out the place, what do we do about the private loan?

Conventional 30 year loan.

so if there is a good reason as to why your score is low and you are now digging your way out and things are going well, it will just take some time, then hard money lenders might be able to get comfortable with you and your credit, more so than conventional lenders.'

Folks, This is a way I can sell properties, for a premium, that may not qualify for a conventional mortgage. 

Keep in mind that mixed properties at the best of times can be a challenge to get conventional financing.

@Brya Freeland if you're going conventional then yes invest through your personal name.

Also note, there are other acquisition + rehab products out there, some conventional.

I won't have the cash to pay for the properties 100% so I'll need at least 1 conventional mortgage.