“In a few months (finishing the final draft now), I’ll be looking to submit a fantasy novel to publishers. What is the best way to pursue this?”
With the comment of “final draft” being said, I will surmise you’ve done multiple rewrites, critiques, and extensive professional editing. If not, then do such first.
Keeping in mind you are not interested in an agent, the best way to pursue publication is to investigate the publishers you are interested in. Check to make sure they are accepting unsolicited submission, and follow their submission guidelines to the letter. Nothing gets a manuscript rejected faster than not following submission guidelines.
You can message (and hope for a reply) from some of their authors. If you get responses like, “They took my manuscript and published it right away,” then you know to stay clear of them. Any publisher who takes a raw manuscript and publishes it without at least one edit run with the author is only looking for a quick buck, and probably will not be one you want to work with. And if you think your manuscript will not need editing after it is accepted, don’t bother submitting to my publishing company.
Depending on how many submissions are received, you could be looking at 2-3 months before they tell you if they are interested or not. Once interested, they will either request the full manuscript (if their submission process only requests a sample) or a quick discussion on what is needed. After both parties agree they want to work with each other, the contract is presented. Being a first-time author means little leverage on the contract, so don’t be too demanding, just make sure you get royalties off of every dime the manuscript makes.
Once the contract is signed, it will be anywhere between 6 months and 1 year before the actual work hits the press. This will depend on the edit rewrites requested and the publisher’s timetable. Remember, they are throwing a lot of money at getting the work ready for print.
Since this is getting a little off topic, I will just end with this last word – Remember you are dealing with a company, and it is not personal. They need to make money if they are to keep going and understanding that they need to get paid on the gamble is a good way to understand why they operate the way they do.