Hi,
Website
Yes, it's your brand online. Start simple - a single page, or 'cover page' will start you off and could contain links to your email, social media accounts etc.
To keep costs down but quality up get a designer to create one using one of the code-free systems that will then also host it for you all for a low monthly fee. Once done you can have access to make any changes to the website for free without paying for every little change. Make sure any images are either your own (or photographs you paid for), or are royalty free for use on your site.
Prices
Don't compete on price as it's a slippery slope down. I would think about your capabilities and what you could offer (within removals) to set yourself apart.
Maybe specialise in high value items, piano's… People will less likely be buying on price for something they value. Odd sized items, heavy loads etc. Or maybe there's a niche in overnight or weekend office removals? Time is money for companies. Work when the rest are sleeping - plus the roads are emptier!
Name and brand
If you haven't already got a name for your business, your chosen niche could help with naming your new company.
Then get a brand designed for your company that is a reflection of your offer. This will influence everything you do, look like, say etc. Your van is your mobile billboard. Make it look good. Vehicle wrapping can be cost effective if you decide to cover the full van.
An obvious point, but make sure your van is always clean and in good condition - it's your brand on wheels! Would you trust a removal company with a dirty van with dented doors?
Marketing
Your specialisation will also help you focus your marketing efforts in one area to start off with. If you do offices, then your focus would be facilities management people/office managers. If you do pianos, then shops that sell piano's, eBay buyers/sellers of piano's who have bought one but need to have it collected.
If you're starting up with no budget see what you can do to get your name out there. Park your van in places that gets seen. I used to see a van one parked over a motorway near me for years.
Anyway, hope that helps.
Good luck!