Verizon Question on Data usage on Unlimited Plans

First a little background, currently family of 4 on an 8gb shared data plan. Never went over but got close quite a few times.

We are looking at the unlimited plans and need help deciding which one.

Mostly we do web surfing, social media stuff and stream some pandora or amazon music or something like that, occasionally there might be some videos in there.

Would the Start Unlimited plan work for our needs or would we need the Play More Unlimited Plan for that?
I am confused on the plans when they say your speeds may be lowered during peak times etc. Does that happen alot? How would it affect general web surfing?

Any help in this would be appreciated!

Thanks!

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