Although I cannot directly recommend you any providers, since I don't have first hand experience, I would say that your best option would be a third party email delivery service.
Such services usually manage your lists, unsubscribe requests etc, and usually reputable providers are whitelisted by all major ISP's, so you won't be problems with getting banned falsely for spam.
The cheaper solution is a VPS, but as you stated that none of you are skilled mailserver admins, I'd side with a third party email delivery service, since getting blacklisted can typically drop your deliverability about 50% just from being on a single blacklist.