Housing authorities generally don't charge landlords a fee to participate or to use their landlord portal. What they'll want from you is a W-9 and a direct deposit authorization, and in many places you set up an account on their portal to see payment statements and inspection results. That side is administrative rather than expensive.
Software is your normal stack. Small landlord property management platforms tend to run somewhere from a few dollars a unit per month up to $15 or so a unit, and none of that is specific to vouchers. What people actually want is a way to track two rent sources against one lease, since the authority's deposit and the tenant's share arrive separately and on different days. Plenty of software handles that badly, which is a real gap if you're building something.
On licensing: participating in the voucher program doesn't itself require a license. What may require one is being a landlord at all, or managing property for someone else. Rental registration, business licensing, and property management licensing rules are set at the state and local level and vary widely, so if your service touches other people's units you need to check your own state's rules with someone licensed there before you sell anything.
Insurance is a standard landlord dwelling policy. There's no special voucher endorsement.
On pricing the pre-inspection walkthrough, a handyman doing a checklist run on a single unit is a couple of hours of labor, so $100 to $250 depending on your market. The value isn't the labor. A failed inspection pushes a landlord into a re-inspection queue that can run weeks, and the vacancy in those weeks dwarfs your fee. That's the number to sell against, and it means you need to know your local authority's actual turnaround time to make the case.