I have tarped for most of my outdoor experience.
One year on a bet (be careful what you say at the pub...)
I spend a full year under a tarp in the bush near my home.
Right now I have a silicone coated 9x12 ripstop nylon tarp.
Marketed as 'aquatarp' on Amazon.
But for a small weight penalty, the coated woven poly tarps you can get at Big Box Stores work.
They don't last as long, but if you are just starting out it's the way to go.
A long narrow rectangle is less useful.
I prefer a rectangle with proportions of about 1.33 to 1 (12 x 9)
1.2:1 (8x10) is about the shortest I've seen.
Had a 9x14 one once.
(1.55:1)
That was several feet of wasted space.
Don't go too small.
You need a reasonable overhang of tarp.
8x10 is the smallest I would use for solo.
If my bag is roughly 2x6 feet this gives me 2 foot overhang at each end, and 3 feet on either side.
In actual use, I'm likely to be off center to have ready access to my pack.
10 x 12 is good for 2 people.
When I helped run an outdoor program, we would use the cheap Canadian Tire tarps, and try to buy blue one year, then green or orange one year.
After a backpack trip, they came back with spark holes, tears, and usually a few missing grommets.
For the winter program they would still do.
And accumulated a lot more damage.
The next fall they would be cut in half, and each pair of people would get one new tarp and half an old tarp.
The latter they used as a ground sheet.
The prevented two events: If they had two new tarps, both would have holes in them by the end of the week, as they wouldn't consistently use one for the roof.
Having a small tarp kept the whole tarp under the roof.
More than one pair of kids has come to grief with all the water that landed on the roof, sliding down onto an exposed edge of ground tarp, and soaking them from underneath.
Site selection is different:
For a tent, you need a certain sized spot, fairly flat, generally about half again larger than the actual footprint of the tent to allow for guy lines.
For a tarp you don't have a bathtub floor, so you look for a spot that either has a very absorbent but is currently fairly dry -- big mossy patch, duff under a spruce tree, or you look for a spot that is clearly higher than the surroundings, or you look for material that has good drainage.
Because it has so many ways to pitch, you can fit into camp spots that are impossible for a tent.
Some of my preferred pitches: Clear weather, rain unlikely.
Support all 4 corners 4 feet
or so off the ground, with enough general slope that if you are wrong you don't have an overhead swimming pool.
Having a tarp overhead means less dew on your sleeping bag.
Variation:
Kite form: 2 kitty corners high, two low.
This sheds water better, but isn't as breezy on a hot night.
Typical pitch.
Mid point of a short side is tied to a tree about 5 feet up.
Opposite two corners are staked down.
This provides head room at one end.
Put the bags at the bottom end to hold tarp away from your bags.
Tree wrap.
I've used this one when caught by a snow storm in winter.
Take off the bottom few feet of dead branches off a spruce or fir.
Tie the middle of the long edge to the trunk about 5 feet up, ABOVE the bottom tier of branches.
Tie the opposite edge to either branches, or to shrubs away from the tree.
The branches support your tarp.
Do NOT break twigs off the top of the branches, as these leave sharp bits that poke your tarp.
outdoors.stackexchange.com/users/2157/Sherwood Botsford
Going back to WW.2.
A shelter half as used by the US.
Army.
This would form a pup tent with 2 joined or a lean to with one.
Sized right for a rain protector over cloths.
Kind of rectangle with a triangle at both ends.
Buttons & button holes at the top.
outdoors.stackexchange.com/users/12302/J Bergen
A rectangular would offer the most choices.
I have used a 8x6 and 9x7 in a half-mid pitch above treeline in the Rockies.
Whether it is rectangle or square, which is also a rectangle, is insignificant since you could do the same pitches with either one assuming the sides are long enough for the coverage you desire.
You would need longer sides if you want to be fully enclosed unless you don't mind cramped space.
Where you run into issues is with shaped tarps that can only be done in 1 or maybe 2 pitches.
outdoors.stackexchange.com/users/11281/topshot
After a lot of thought, I don't think that there are any shape configurations that would be limited to just a square or just a rectangular tarp.
However, when you are sleeping under a tarp, either on the ground or in a hammock your body is in a rectangular shape.
I use a 5ftx7ft tarp
and if it was 7ftx7ft square tarp it would just be extra weight to carry.
outdoors.stackexchange.com/users/8794/Charlie Brumbaugh
When it comes to flat tarp shape, there is no right or wrong answer.
Both shapes can be used to make simple roof, lean-to-type or a fully enclosed tent-like structures.
There is a ton of information about different pitches at: http://equipped.com/tarp-shelters.htm
There is also this question about tarps and wind:
What is a good tarp setup for very high winds above the tree line?
outdoors.stackexchange.com/users/5836/StrongBad
I'd like to try tarp camping.  3m x 3m (9ft x 9ft) and 3m x 4m (9ft x 12ft) tarps of differing material are plentiful and many are even affordable.  Which tarp shape is more versatile in the number of setup configurations?    Configurations should include a simple roof, lean-to-type or a fully enclosed tent-like structures.  All weather conditions should be considered also.  I know there are other shapes but they seem to be intended for specialized configurations.   So Square or Rectangle?
Are square or rectangular tarp shapes more versatile?
outdoors.stackexchange.com
<hiking><camping><shelter><tarp-tents>
outdoors.stackexchange.com/questions/16445
outdoors.stackexchange.com/users/11800/B540Glenn
Whether it is rectangle or square is insignificant since you could do the same pitches with either one assuming the sides are long enough for the coverage you desire. Both shapes can be used to make simple roof, lean-to-type or a fully enclosed tent-like structures. Both shapes work well, though rectangular offers more options.
Both shapes work well, though rectangular offers more options.