Hi Ben,
What you need for a chute(s) depends on the application. The heavier a rocket, the more critical it is that it come down in a controlled fashion. The faster it can go, the more critical it is that the recovery system can take very high loads.
On the largest projects, people use man rated chutes or their equivalents or near equivalents without the rating. On the fastest projects, the drogue chutes may be designed for successful deployment at speeds exceeding mach 1.
At the smallest and lightest end, hobby rockets have used tumble recovery, streamers, plastic chutes, helicopter recovery...
The recovery system needs to be sized to the intended rocket. One is typically aiming for a descent rate of between 15 and 25 fps. The rate should be slow enough to essentially ensure that there is no damage to the rocket upon landing (or minimal, in certain special cases) and minimal risk of damage to whatever the rocket might land on!
One can see that if one targets 20fps descent rate, and the flight is to 500', then the rocket has 25 seconds to drift under main parachute. It won't drift all that far. But, if the flight were to 10000', the rocket would have 500 seconds to drift... That would be a problem! Wind speeds are higher at greater altitude above ground. The recovery crew would be in for a bit of a drive.
So, for flights which go at least a moderate altitude, one doesn't really want to open the main at apogee. But one also doesn't want to delay opening any recovery as the rocket will be gaining speed quite efficiently on the way back down! The shock of opening a main at high speeds would quite possibly rip the rocket apart and at least would do some damage. We absolutely do not want to rain parts down on spectators!
At apogee, the minimum we do is break the rocket apart. We want to render it a non-aerodynamic structure, without stability. This way no matter what else happens, the rocket cannot attain high speed on the way down. Some heavy fiberglass rockets have a terminal velocity in the hundreds of miles per hour. They can go completely subterranian on impact. This situation is to be absolutely avoided!
Usually, but not always, breaking the rocket apart at apogee also deploys a chute.
A small chute intended to provide a controlled but fast descent is called a drogue chute. These are typically very small chutes compared to the size of the rocket. They are also often relatively solidly constructed. If a rocket launch goes haywire for some reason, apogee may be accompanied with rather high horizontal speed... This stresses the recovery system and the drogue needs to be able to take it. Ditto the attachment points, lines...
If a drogue is being used, then the main does not have to be able to take high speed deployment. Such a main does not need to be as beefy. Drogue chutes are typically sized to control the rocket descent at somewhere between 50 and 100 fps.
As for the chutes themselves, at the smallest end, a simple plastic chute may suffice. At the biggest end, a commercial cargo chute may be in order for the main, and the drogue would be suitable for hanging off the back end of a dragster or a jet, or to slow the descent of a bomb released at high speeds.
Better chutes are typically made of rip-stop nylon. As the name implies, the intent of the fabric is to prevent a tear from spreading. Being nylon, these chutes should not be left for long exposure to sunlight. Sunlight (UV) degrades nylon.
Better chutes have stitched shroud lines. The picture you posted appears to have shroud lines that are stitched near the edges of the canopy. This is good. There are multiple ways to stitch the lines onto the canopy and some are definitely better than others.
https://spherachutes.com/construction.asp - Read this over; it will likely answer some of your questions.
I apologize if my post was aimed at too low a level. I just figured to start with some of the basics.
Gerald