LLC is a Limited Liability Company.
LLP is a Limited Liability Partnership.
You cannot make an LLP of a single partner - you must have 2 or more. You can, however, make a single-member LLC.
As to the taxation - that same web page you linked to in your question has this to say:
A single member LLC disregarded for Florida and federal income tax
purposes is not required to file a separate Florida corporate income
tax return. The income must be reported on the owner’s return if the
single member LLC is owned, directly or indirectly, by a corporation.
The corporation must file Florida Form F-1120, reporting its own
income and the income of the single member LLC, even if the only
activity of the corporation is ownership of the single member LLC.
I.e.: if your LLC is classified as a disregarded entity and you (the individual) are the only member - you will not be required to pay Florida income taxes.
Just to remind you - there's no such thing "W2 contractor". There's "employee". Once you stop being employee and become a contractor - you lose some benefits and protections. You will also have to pay your full FICA (as an employee you're only paying half, your employer pays the other half). That is the reason why contractors get higher hourly pay.