Over 10 years experience in the field of email marketing. I have co-founded and actively run a number of businesses that have email marketing as their core focus when it comes to marketing products, services and information.
When I begin the process of building my email lists, I always start with solo ads.
Take a look at buying some solo ads in your niche space. Facebook has a number of groups that provide solo ads and you can select people with an existing email list of subscribers who are related to your niche. There are also websites such as warriorforum and udimi you could explore
Always check out the reviews of the provider and start with a small test purchase to see what kind of results you get before spending your full budget on one order
As your list starts to grow, you can also send emails to your list with incentives to share your newsletter with their friends and family who may also be interested in joining your list
Do not buy email lists - it may seem quicker but you cannot put a price on opted in subscribers vs bought lists (not to mention the compliance/can-spam implications you may face if you start emailing subscribers who never asked to received your messages)
Hope this helps!