This is bringing back memories

I've been low key wanting to get some hermits again but have been being good and not doing it. Even though I have an empty 20 gallon long tank just begging for some occupants...
Anyway, hermit crabs are much harder to keep than those beach places that sell crabs make out. And of course they downplay it, because who would impulse buy a crab while they're on vacation if they knew it meant that they had to also buy $100+ in supplies?
Habitat
So, first things first - the habitat. A ten gallon aquarium is an ideal starter home for crabs. You can house up to four medium crabs in a ten gallon (I'll come back to this later) so it makes a great space for a small colony.
There are lots of options for substrates. Eco earth coconut fiber works fine, I used it with my crabs. But sand works too, and I ended up just going with sand. I found it to be less mess. Plus it's less expensive. A 50 pound bag of play sand will work fine for your crabs, doesn't cost too much, and will last you a long time. Substrate depth is also important, because a crab needs to be able to burrow down into it to safely molt. At least six inches deep is the minimum. For larger crabs, it may need to be deeper.
Habitat humidity is key. Crabs need a very humid environment to keep their gills from drying out, which is very nasty way to die - and is unfortunately how most crabs meet their demise. After all, they're sold with those mesh cages you showed pictures of before, and if they're sold with those cages, they must be fine, right? Well, those cages can of course in no way hold humidity, so the crabs dry out, and die.
So, that said, humidity in their crabitat should be 70 to 80 percent. The damp substrate will help with that. A glass lid for the aquarium instead of a mesh one also helps to keep the humidity in. If you're really having trouble getting it up, you can set up a bubble pool.
To measure humidity, you must purchase a hygrometer. It's important to calibrate it to make sure it's reading accurately.
Temperature is also very important. Ideally you will keep it 78 degrees in the tank. 65 to 85 is the temperature range that they can live in, and the tank should always be in this range.
You'll also want hiding places for them. Now, crabs are naturally social and happily pack in together (again, I'll be coming back to this) so you don't really need a ton of hides for them. One or two is fine.
Also, they love to climb. On some islands they're referred to as Tree Crabs because of how much time they spend climbing around in the trees. So, you'll want to put in things for them to climb, like vines and branches, etc.
Food and Water
First up, water. This would seem simple, but hermit crabs need access to both salt water and fresh water. For the salt water, you can either buy salt that's made to add to saltwater aquariums and make up your own, or, now that pet stores are finally wising up to the proper care of hermit crabs, some stores will sell small premixes bottles of saltwater for them.
Don't use tap water for them - if your water is chlorinated, the chlorine is harmful to them. Well water can be 'heavy', and contain things that are bad for them as well. It's better to buy a gallon of distilled water from the store.
Water should be offered in a dish deep enough that they can fully submerge, but make sure you have something in the water dish that allows them to easily climb in and out.
Next, food. Nowadays there are commercial diets you can purchase for your crabs. When I had mine, a lot of these diets actually contained things that could kill crabs, so I had to make my own. Making your own is a viable option if you don't want to purchase.
Here's the recipe I used to use:
2 large cuttlebones
1 cup dried rice (any non-instant type)
1 cup unflavored oatmeal
1 tsp. sea salt. NO table salt!
1/4 cup dried plankton, krill or any other very stinky dried sealife
2 tablespoons spirulina powder (you can buy this at almost any health food store)
It all gets mixed together and ground into a powder.
In addition to their staple diet, you should also offer things like fresh fruits and veggies. Fruits that they would find in their native habitat, like mangos, papayas, and coconuts are always a big hit. They also like meat, believe it or not. Freeze dried shrimp and plankton, etc, also go over well.
Shells
So, your crabs will need new shells as they grow, or as the old ones wear out. NEVER use painted shells. The crabs don't like them, and the paint contains things that are toxic to them.
Instead, go with natural shells. There are tons of types of shell to choose from, and each crab will have its own preferences. As a rule of thumb, you want to keep three or four appropriately sized shells per crab in your crabitat. And appropriately-sized shell is one that the crab can fully fit into and seal the opening of with its claw.
Crabs also tend to prefer shells that are lined with mother-of-pearl.
Probably the easiest way to tell what size shell you ought to get for your crab is to measure the one it currently has on. Measure across the opening when the crab is pulled into the shell. Or, use a set of calipers to measure. That will tell you what size shell it's currently in. Then, go ahead and buy a few that are a little larger.
Most crabs (and I'll come back to this) like a shell with a circular opening.
Friends
I know you said you only plan to get one crab, but really you need more than one. At least three, really. If you can only get one crab, don't get any. Hermit crabs naturally live in colonies. In the wild, you see them in groups of one hundred or more. They pile together to hang out. A single crab is very lonely. Often, they become fairly inactive. And, a single crab actually has a shortened lifespan - they die sooner because of loneliness.
Three crabs is basically no different than one crab, care-wise. I'm not sure why your parents would object to three instead of one, since they take up the same amount of space and it's not like they would be making more mess or anything than one. But if for some reason they just won't allow more than one, go with the betta instead.
Species
On the topic of friends, did you know there are different species of hermit crabs that are commonly sold in pet stores? Yep! And each crab needs a friend of its own species, so it's important to pay attention to what species you're buying.
The one you're most commonly going to find for sale is the Purple Pincher. This guy usually has, as the name would imply, a large purple claw. He also has rounded eye stalks.
The other species you might find is the Ecuadorian. He has a smaller claw than the purple pincher. His eyestalks are also more elongated, and are more oval than round. These guys tend to prefer shells with more slot-shaped openings - they tend to be pickier about shells than other species! They also are very active, more active than the purple pincher. They also often make noise! They talk to other Ecuadorians with chirping, squealing noises fairly often.
There are other species too, like Strawberries, Blueberries, Violas, Indos, Ruggies, etc. But you're unlikely to find these at a small beach stand selling crabs, or even in a pet store. Some of them are also harder to care for, so I wouldn't recommend them for a new crab owner.