What are the free basic checks Trusted Advisor provides? Is it worth to go with paid plan?
The free checks include security checks and service limit checks. For service limit checks, an example would be, are you approaching any of the "soft limits" on things like, for example, the number of EC2 instances you can have launched at a single time?
I doubt it would generally be worth updating to the Business or Enterprise support plan just to get the expanded Trusted Advisor. But if you have a use case that calls for one of those plans, it is one more feature that you can take advantage of.