How little can I put as my budget for Google AdWords for a very small company and still be effective?

Id second Stan on getting an expert to set up your account and run it for at least 1 month. Nowadays adwords agencies and consultants offer 30-day money back guarantee so you can try them out and hold them to their word that they will make you profitable within 30 days. Good luck!

I would recommend you to start with $25/week where you can select only relevant and potential keywords (sales keywords) with an exact keyword match type to avoid any unwanted clicks. Further thoughts: If you really want to be see effective results though you have a small budget then you need to be an AdWords expert, brainstormer, creative, and landing page optimizer: Four important aspects to see desired success and ROI from Google AdWords PPC Campaign: Targeting the right audience (You need to be an AdWords expert for appropriate campaign settings) Choosing the “Sales” keywords (You need to be brainstormer to identify the potential  keywords which will be going to type your prospects for finding your services/products) Creative Ad-Copies (You need to be a creative while writing ad-copies. Your ad-copies should have the power of 4C which are - Clean, Clear, Concise, and Call-To-Action) Selecting  the right landing page and displaying only significant information  about particular product/services you wanted to sell. Remember, landing  page quality score directly affects ad-position hence you need to be an experienced and an expert landing page optimizer to see the highest landing page quality score. Hope this helps!

If you get the initial setup right, either by yourself of with the help of a consultant, then the question will see a reversal. How much more benefit do you expect? You can scale up accordingly after that. The initial trial-and-error process will prove to be highly insightful. I've seen businesses start off with spending even $100 a month and then scale up to $2000 a month within the first year itself.