There effectively is no "best cheap seo service" .... Think about your question a little... If I can rank someone cheaply why would I charge a cheap rate?
Part of being a business man is knowing what your worth. I can rank my clients for just about any keyword but, I charge appropriately for my services. Stop looking for bargains and look for quality or ROI as some have mentioned.
... Think about it. All these services that charge $50 or $200do you honestly believe your actually going to rank? NO. Occasionally some people strike it lucky in a low competition niche or others claim it's a high competition niche but, don't actually know how to determine competition. In short, the odds are 1 in 1,000,000 that you will get a working seo service on the cheap.
Sure, you might move a couple positions, but as everyone knows if your not top 3 of page 1 you're not getting traffic. So #4, 5, 6, 7, 8, 9, 10.... hardly mater.