If you're new, don't start by asking how to send 10k as cheaply as possible. That usually leads to burnt domains, poor data, and zero replies.
Split the stack into three parts: leads, verification, and sending. For leads, Apollo, Snov, Hunter, Prospeo - they can work, but don't buy a massive list and blast it. Build a tighter ICP first. For verification, run every email through a verifier before sending. Bounces wreck your sender reputation fast. For sending, use separate domains and inboxes, warm them slowly, and never send from your main company domain.
10k a month isn't crazy, but only if you ramp up properly. With brand new domains, start much smaller - test 200-500 highly targeted contacts, see if the offer gets replies, then scale. Volume won't fix bad targeting.
Something like SMTPProvider can help on the sending side - SMTP sending, domain checks, controlled limits, bounce visibility, and not wrecking domains while testing. But still spend more time on list quality and the offer before worrying about sending 10k.
Cheapest stack isn't always the cheapest long-term. Bad leads plus bad sending setup gets expensive quickly.