Use this strategy that have worked for me.
Get a primary dedicated server at around $35, install WHM/Cpanel to it. You can install trial version if your budget is tight to save money. Alternatively you can directadmin which is available free. Just get hosting provider to install for you.
Set RDNS and DNS to the server. Name this as primary server.
Set domain name as xyz.com
Install Interspire or other mailing script (need help on this let me know).
Next get a couple of Linux VPS hosting plan which allow SMTP, look on BHW, there are many. Usually cost around $6-$12. Setup domain as smail1.xyz.com (shared server 1), smail2.xyz.com (shared server 2), etc. Hope you get what I mean here. Setup about 5 different server. Each server should allow you to send 100-200 emails per hour. Remember to throttle the sending speed per server.
Then set in your primary server all the above delivery mail server. The primary server will be use to handle feedback and bounces. This is why we are using dedi server here.
5 x VPS hosting= $30 - $60 = 1,000 emails per hour. 24 hours = 24,000 emails per day. If you have multiple IPs, then setup on the VPS to increase sending capability
1 x Dedi = $35
Total cost between $65 - $95 monthly
If you noticed that soft bounce rate rises then you should change the VPS and setup with new domain. Spamahaus would blacklist domain and IP. But with the above setup, your main TLD is not blacklisted so you can still change your server.
Can't really type too much here, in case i miss out on something or you have question, feel free to ask.
Take note that public emails like Gmail and hotmail will still put your email in the junk folder by default unless receiver whitelist you.