Excellent question (and excellent answers here too). I'm 18 months into my start-up. That's 18 months of learning what is essential to survival and what is a waste of energy and space.
Here is what is helping me most:
1. Communication essentials: Business cards (moo.com), laptop, phone, and Internet access. No explanation necessary.
2. Memberships in free or low-cost online media and networks (like this one). Online (in order): 1) Gmail, 2) LinkedIn (especially groups), 3) Meetup, 4) Twitter, 5) WordPress, 6) Constant Contact, 7) Facebook. Use these to find in-person opportunities to network and prospect. These tools are your lifeline to building an online presence, prospecting, and researching. Also vital: Testing your product or service idea.
3. Bookkeeper or good bookkeeping software. I cannot emphasize this enough. CASH IS YOUR BUSINESS. If you don't have a budget and cash flow projection, you don't have a business. Period. You MUST make this the heart of every activity and every day. If you suck at it, find someone who is good at it and spend the money to get them to help you.
BONUS: Listen to podcasts like "Entrepreneur on Fire" and subscribe to free resources like Jeffery Gitomer's "Sales Caffeine."
As a bonus, here is what took up space in my toolkit (now jettisoned):
1. Big bucks on a graphic design firm to do my marketing media. This is not for starting up; it's for later. Use free or low-cost design services or templates. You want to test your actual business idea first before investing thousands of dollars in a design company.
2. Apps, apps, and more apps. I went app crazy in the beginning, buying buckets full of "productivity" software. It ended up sucking up too much time and I settled on Evernote and Google Spreadsheets because they're familiar and they work for me. Big apps are for later.
3. Coffee meetings. OMG. I wasted hours and hours and hours having coffee with my "network," which amounted to a lot of people who could pat me on the back but who could neither buy from me nor refer any business. Affirmation is great, but too much of it will run your right out of business. Find a network of entrepreneurs in your community and spend more and more time with people who can buy from you. It's the only way to grow.
I'm happy to visit with you from the trenches. Please give me a call if you like.