Q - I have heard some say that self-publishing is the best way to go, especially for first timers? Should a new author self-publish and is it more costly?
A - First of all, this questions suggests that the writer does not have a clear undrstanding of the differences between a royalty publisher and and a subsidy publisher. So just to clarify that point, with a royalty publisher, you do not pay anything--the publisher pays all the expense of publishing the book and distributing it. (Except for any expenses you choose to incur in promoting the book youself.)
With a straight subsidy publisher, you pay all the cost of printing and distributing the book--which answers the question of whether it is more costly. You will also find some publishers that fall into other categories--which I call co-op publishers. They offer deals where you pay part of the cost and they pay part. The amount you pay will vary a great deal with this type of publisher--so shop around.
As far as whether self-publishing is the best way to go for a new author, it really depends on a lot of factors. If it is a book with a broad appeal (fiction or nonfiction), then look for a royalty publisher first. If the book is well-written and has a broad, definable audience, a royalty publisher is your best choice. If the book has a very specific or narrow audience, then you may have to self-publish.
If you have a good "platform"--meaning you have a well-established speaking ministry and good contacts (such as an organization)where you can sell a lot of books yourself, then you can often make more money by self-publishing. If you don't know how you are going to sell the book--or to whom--then self-publishing is not the way to go. You don't want to end up with a garage full of expensive books you can't sell.