They should all work well with Gmail, since it's the most popular recipient, and all popular solutions have deliverability statistics. I'd guess that using Gmail itself via its SMTP service [1] would be the most reliable overall.
Edit: Looks like you can, but Google says it's "not recommended." Also, you need to be a paying Apps member to use the service from what I can tell. Not sure if you can if you aren't a paying member.
Scroll down to Step 6, where it shows "Any addresses (not recommended)"
Apparently, it works, but with some notable caveats, like: "If the envelope sender is not in one of your domains, the system changes the envelope sender from user@[domain you don't own] to postmaster@[your domain]"
The issue would likely be the limit on messages per day. Google spells this out for paying Apps members (https://support.google.com/a/answer/2956491#sendinglimitsfor..., see "Limits Per Customer")
They don't say what the limit is if you're using SMTP relay as a regular gmail user. I suspect it's much lower.