> what are good milestones to use to trigger payment?
What are the key features of your application?
- create account, log in, log out, edit user details
- list items for sale (sellers)
- search items (buyers)
- end to end transactions

> But again, how is "completion" defined?
You test it.

If you've written the requirements clearly, it should be pretty obvious what needs to work and how you would test it.
Like for example, you'll have statements like
- A user will be able to create an account
- A user will be able to change their password
- User information will include home address and phone number.
I like numbered paragraphs with only one "will/shall" imperative statement per paragraph, along with any additional descriptive prose to help with understanding. Yes it will be a dry read, but at least everyone will know where they stand.

From that, you can derive a list of tests which you expect to pass at each release.

With the first alpha release (possibly even before then), you'll need to agree on the process for raising bugs against specified releases.

> --> So say for example we have a list of items in the Scope of Work
> and as each item/a few items are completed we hand over the money?
Except it would be a flat rate. Even if nothing seemed to happen in one week, you'd still hand over the agreed weekly amount. Maybe there were some hard problems which slowed progress down. Likewise, other weeks will show massive progress. So long as the "moving month" average looks like it's on track, there shouldn't be much cause for concern on your part. But at least you'll have a record of what was being done.