I strongly recommend going with a service. Unless you are going to send a huge number of emails, the costs of hosting and your time dealing with the hosting and the server will exceed the costs of using the service. Plus your spam and compliance issues are handled.
If you are going to roll your own, hosting is wise. Most hosts have fairly tight terms of service around spam and do not tolerate hosting a spammer. If it becomes an issue the burden of proof will be on you to demonstrate that you are being a good netizen.
--> You might try Amazon EC2 for cheap, reliable hosting. The capacity on demand model might be effective for your kind of workload, which is typically light, but occasionally and predictably heavy.
If you are going to do this then use a good list manager. MailMan is open source and runs on Linux, but I am not sure if it lends itself to one-way bulk emails. There are other open source or cheap packages but I have no recommendations.
Generally the hosts don't count emails sent, but rather they count data transfer. The biggest factors are how many addresses on the lists, how big the emails will be, and how frequently the blasts. If you are sending a couple of thousand emails once or twice a month you need the list manager, but probably won't have any data transfer issues.