I have a finish carpentry/woodworking business that has kept me extremely busy for the last 7-8 years, I started from scratch here and have never advertised.
If you can be professional, call people back, show up on time, and do good work you will have all you can handle once word starts spreading.
You’ll have to check local laws as to what you’re allowed to do. Some states it’s a free for all, some are extremely restrictive.
Here you have to be a licensed contractor to pull a permit, and replacing an exterior door is supposed to be permitted. You can’t get a contractor to even give you a price on that, so the handyman type guys do it sans permitting.
If you’re doing non electrical/plumbing/structural stuff, all you need is a worker’s comp exemption, which requires filing and LLC.
Print up some business cards, make sure you have a local area code on your cell or get a work line app, and have a professional voicemail and at least a business gmail account. Facebook and Instagram are all most people look at these days besides the older crowd, so you don’t need to dump a ton of $ on a website.
I’d find a contractor you can get along with and refer them work that you can’t handle, they will send you stuff left and right. I work with 4 or so interior designers that are awesome as well.
I don’t take deposits to hold a place on my schedule, but for anything from $1,000 - $10,000 I take 50% for materials when we start and the balance at the end. Make sure you can accept credit cards, Square has been great to deal with and has no monthly fee, I use Invoice2Go for my estimates/invoices.
I have a shop, but the best thing I’ve ever done was buy a 6x12 enclosed trailer than I can hook up and head to a job with everything I’ll need in it. Back stocks of fasteners, ladders, stuff you don’t expect to need.
Regarding customer base, don’t try to be the cheapest, and stay off Home Advisor, Angie’s List, Home Depot installers, etc. You don’t want the people that are shopping half a dozen guys for the “best price”. They will be a pain to deal with, expect you to do stuff for free, etc. You want people who have heard you do good work and will pay your rate and wait until you can get to it.