Hello gobbly2100,
Yes thats true, on shared hosting environment you will be restricted to maximum 300 emails an hour. Also, you can check out for the provider which supports PHPlist as there wont be any per hour limit on newsletters.
before moving to a dedicated box, I will suggest you to check with the VPS packages
Please let me know if you have any more queries in this regards, I will be glad to assist you.
Thank you.