Hi Dan, welcome aboard and sounds like you are about to embark on an exciting adventure!
Marketing strategy wise is always going to be dependant on your type of business, and what works for one may not work for another.
But leaflets are a great inexpensive way of getting your name out locally. Personally I'd be peeved having to open an envelope to look at junk mail. If I'm in the market for a removals firm I'll keep your flyer, if not it will go in the recycling. I would imagine most people would google a removals company so a fast professional looking website is a must. Also don't forget Google My Business listing, which will give you a right hand panel in the Google search results.
Directories are ten a penny and we all want your cash
Down to you if you see perceived value. But even free listings do have value, as long as all your details are correct. Google and the other search engines use these as "citation" references, ie you are who you say you are and offer a little bit of help for your own website.
Most decent directories also have customer review facilities, so as soon as you get genuine customers (please don't fake them!), having reviews about your business on multiple sources builds credibility and a positive web presence.
Likewise ensure you have a Facebook business page and LinkedIn. Don't be salesy, be social. Facebook marketing can be very powerful, cost effective and very targeted. Google PPC is also very powerful. But it's easy to burn through money if inexperienced and people will try and fleece you are 20% of your budget to manage it for you. Works for some, not for others so maybe some trial and error.
Another good way for credibility is industry associations, so maybe research BAR membership and see if it viable for you. BAR are part of the Chartered Trading Standards Institute Consumer Code, so it means you can put a nice Trading Standards and BAR logo on your wagons, website and marketing literature.
There's a starter for 10, but very best of luck, let us know how you get on and feel free to ask any questions 