After doing the math (read: using the internet), I've determined that 24L is a bit over 6 gallons which by all means is more than enough for a healthy betta. 2.5 Gallons (9.5L) is the suggested minimum, so anything over is exceptional.
Should you go forth with a tank of this size, you'd need to cycle it before adding shrimp or corydoras. Both are quite sensitive to water parameters. However, I don't know if you'd be able to add corydoras to a 6 gallon tank as they're schooling fish and prefer groups of three or more. As such, I think the bio-load would be too great for the tank. Shrimp are fine, though, and you could have several. Same with ADFs and snails.
And finally, to answer your primary question, you may also need a cycled tank before adding live plants. Maybe. I suppose it depends on how you clean your tank. If it's constantly being uprooted it will die. If I'm not mistaken, Java Fern / Moss, Red Ludwigia / Moneywort, and Amazon Swords are all recommended plants, but again, I don't know how these apply to uncycled tanks. For fake plants, always go with silk; Plastic plants can easily tear your betta's fins. With either, though, you have to make sure they don't contain wire or fragrances, and won't bleed. As far as preference, your betta will appreciate any plant or decor - the more crowded the better.
I hope I'm providing useful information. I should probably take a break from the internet.
Lol, I try. I'm just a little apprehensive about giving information as I'm still learning a lot myself. It's a good thing you're looking into fishkeeping before making your purchase, though. Knowledge is power. Woo woo.
Yay go me :p I've never actually been one to research this much, I'm strong minded and usually if i want something I'll go right out and get it lol So im quite proud of myself for taking the time to google :P
Live plants are a lot better than fake. I'd rather have nothing in my tank than ever go back to fake decor or plants. Plants provide oxygen and if your tank is planted well enough it uses the fish poop. It cuts back A TON when it comes to water changes also.
You can add plants right away to a new tank. Cycled or not. It actually jump starts it.
I go hardcore when it comes to plants. But very very easy plants are:
Be very very careful when getting plants from petco/petsmart. like 95% of them arent true aquatic and will die. If you need any help with plants or set up ask away!
The look of live plants is so much nicer than that of fake plants.
Like the poster above, I would rather have no decor than fake decor.
I suggest this. Take 10 bucks to Petco/PetSmart and purchase one fake plant and one live plant.
GO ahead and put them both in alternate sides of your aquarium. You'll come to your own conclusion on which you like more.
As far as what fake plants to get, bring with you to the pet store, a piece of panty hose, a long strip that has no runs. As you rub the pantyhose across all points of the fake plant, this will tell you whether or not it is abrasive enough to harm the fins of your betta fish. This holds true with rocks, gravel, and just about anything else you might plan on introducing to your betta's tank.
If you decide you don't like the idea of live plants or plastic, also consider driftwood.
Driftwood and live plants go together very well, and it looks fantastic in almost any aquascape no matter what the size (and bettas, shrimp and corys LOVE it!)
Just know, that if you decide to go with plants, you're going to possibly need a slightly more intricate lighting setup than no light at all.
In a 6 gallon tank you can't add corys.. corys need to be in groups of 3 or more and should be in a minimum of a 10 gallon tank. Cherry shrimp will work fine but don't be surprised if your betta thinks they are a tasty snack LOL.
For plants I would go with silk plants if its your first tank. Sometimes adding live plants plus dealing with all the other new things that come with fish keeping can be too much.
If you do want live plants I would go with java moss, java fern, anubias, crypts, sags, vals, amazon swords.. just to name a few.