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I think the best way to cost effectively advertise your service is as follows:
1. Make your own WordPress website that explains what you do, your unique selling propositions, the benefits of working with you, quotes from your previous customers, a call to action (e.g. get a free quote), and a contact form. You should also try to offer something of value (e.g. an ebook) in exchange for their name and email address.
2. Make sure the website SEO is dialed in. See https://www.askbrien.com/questions-and-answers/traffic/.
3. Advertise on any of the free platforms. One of the best ones is Craigslist. The key to advertising on Craigslist is to do it twice a day every day for the life of your business. Never miss a post, never miss a day no matter how long it seems you have been doing it without a result. I have gotten a lot of huge deals through Craigslist by just being persistent.
It appears your audience is nationwide? Cost effective can mean limited budget or return on investment. As to both I would look to social media. You can try YouTube or Facebook for advertising. Facebook ads can begin at $5 per day. YouTube can be effective if you gear your ads to your target market. As to effectiveness there is no magical formula. You need to test and test and test. When something works put your money into that test that was successful. Success can be earning $1 more then you paid for some people and others need more.