There are a bunch of questions you need to think of, and the final answer will depend on all these various factors...
How long do you want your tarp to hold up?
Is it simply for a single-use construction to keep some folks dry during an outdoor party? Is it a permanent cover that will stay (and have to hold up) for months or even years?
--> Cheap plastic might work in the short term but will deteriorate quickly, especially if you don't invest in UV-resistant product.
What winds are you building this for?
How sheltered is the tarped location? Does it have to hold up during high winds?
--> The more wind forces you expect the higher your need for a proper sturdy tarp.
Once-off or repeated setup?
Do you set this up once and then leave it in place, or do you plan do use this as an easy shelter to take with you on camping trips?
--> If you want to re-use your tarp you'll be happy to have a good sturdy tarp with nice grommets/loops to help you set up. If it's just a once-off thing you can work around the lack of grommets with various tricks (e.g. using a stone to tie your rope around).
Will there be snow loaded on the tarp?
If you expect snow loads you'll need a sturdier overall construction.
Do you want shade or simply rain-protection
--> Obviously if you want shade then don't pick a transparent tarp/plastic, but a darker colour. Take care that if there is not good ventilation beneath then a dark tarp / tent will heat up the air below it quite considerably...