[laumars]

Why not just install Roundcube[1] on top of your preferred MTA? It's free and it's going to be more polished than any $500 bespoke project.

[1] http://roundcube.net/

[drchaos]

For $500 one could easily install roundcube, add some branding to the default skin, and still have some budget left for ramp-up support or doing some additional tweaks.

From this point of view, the project and budget is actually quite reasonable.

[fduran]

That was my first thought too: a domain + Roundcube + Mailgun