Do you just go for the HUD amount or do you price it lower?

It is simpler and lower cost.

I'm imagining a lot of competition at the higher end valued properties and almost none on the lower end.  

A portfolio loan might also be a good idea, provided you have multiple properties to bundle together; this can help lower the down payment.

:Class A Properties:Cashflow vs Appreciation: Typically, 3-5 years for positive cashflow, but you get highest relative rent & value appreciation.Vacancy Est: Historically 10%, 5% the more recent norm.Tenant Pool: Majority will have FICO scores of 680+, zero evictions in last 7 years.Class B Properties:Cashflow vs Appreciation: Typically, decent amount of relative rent & value appreciation.Vacancy Est: Historically 10%, 5% should be applied only if proper research done to support.Tenant Pool: Majority will have FICO scores of 620-680, some blemishes, but should have no evictions in last 5 yearsClass C Properties:Cashflow vs Appreciation: Typically, high cashflow and at the lower end of relative rent & value appreciation.

For instance, if lower-end housing is purchased in Texas with an ARV of $70,000 to $90,000, you may be able to negotiate a deeper discount—say, 65%.

Expenses (both transactionally as well as operationally)  disproportionately impact lower priced assets.

:Class A Properties:Cashflow vs Appreciation: Typically, 3-5 years for positive cashflow, but you get highest relative rent & value appreciation.Vacancy Est: Historically 10%, 5% the more recent norm.Tenant Pool: Majority will have FICO scores of 680+ (roughly 5% probability of default), zero evictions in last 7 years.Class B Properties:Cashflow vs Appreciation: Typically, decent amount of relative rent & value appreciation.Vacancy Est: Historically 10%, 5% should be applied only if proper research done to support.Tenant Pool: Majority will have FICO scores of 620-680 (around 10% probability of default), some blemishes, but should have no evictions in last 5 yearsClass C Properties:Cashflow vs Appreciation: Typically, high cashflow and at the lower end of relative rent & value appreciation.

The former provides a much lower return on equity but is simpler and easy to achieve over the long run.The latter is much more time consuming and risky, but provides high returns and a lot of tax advantages. 

As an example section 1250 gain is taxed like ordinary income, in contrast generic capital gains has a much lower rate.