First I'll start off by saying these creatures are highly intelligent and very cheap easy to keep and require only a cheap simple set up. As long as you keep up on husbandry and water changes that keep nitrates and phosphates at a safe level it's as simple as feeding and sitting back and watching these amazing creature do what they do.
Although you can go small with the mantis your color options will be red, green or brown. Plus small ones aren't as fun because they hide in the holes of rocks, are not as personable and won't put on a show breaking crabs into pieces like I'm sure you have seen videos of. Although the likelihood of having a fish in the tank with them greatly increases. Also parameter changes, say slightly high phosphates and nitrates and prolonged periods of time between feedings are tolerated better by the small mantis then the large.
Nothing wrong with what I just said just not my cup of tea, if I'm going to dedicate an entire tank to a mantis shrimp and I do. It's going to be large, in charge, greet me when I come to the tank, follow me around the tank and put on a show which my peacock mantis shrimp infamously named Clubber Lang surely does. I have friends on FB every Sunday waiting aniouxsly for the new Cubber Lang video to be uploaded.
For Large Mantis 5"+ you have the zebra mantis which is a spearing type mantis and my all time favorite (having one) which is where you will see a majority of pictures and articles about is the Peacock Mantis shrimp. To touch base quickly on the zebra mantis the can easily reach 12" plus and have to have a fine sand substrate depth that matches the length of their body. So your talking about a few hundred dollars of sand to provide a 14"+ deep sand bed plus they only eat fish, that'll get expensive.
Now back to the peacock mantis which is what I highly recommend to get is the peacock mantis shrimp. Here is why they get large enough to take on any sized crab you can buy (what a show that makes), they are the most colorful and vibrantly colored, will take the "materials" you put in the tank and organize it to their liking (cool to watch), and most personable the best way I can describe that is think of him like a dog following you around watching your every move. The downsides you can't put fish with them it's only a matter of time before the fish swims past his hole and becomes dinner. If the fish is too large to eat it's still going to get a deadly blow to the head and die, must provide building "materials" not only to decorate but also for when they moly their shells, more sensitive to phosphates and nitrates so keeping them in checks by cleaning up the tank and routine water changes is a must and their diet is more specialized. They have to get a crab at least once a month or their risk of a club falling off is a greatly increased ("if you don't use it you lose it") a crab weekly is better and way more fun but not a must. What is a must is once a week of not twice if your doing one crab a month a a larger sized piece of food that must be soaked in selcon if you would like to keep your peacock mantis alive for any long period of time. Mine gets a crab every Sunday and 2 good sized pieces of selcon soaked krill every wednsday. I think I covered it all if I missed something about the mantis itself ask or I'll add it in another reply.
The following tank set up goes for both small mantis and peacock I'm not going to list stuff for a zebra mantis because your sized tank can't support one.
Tank equipment list-
1: RO/DI Water mixed to 1.025-1.026 salinity. Do yourself a favor and get a refractometer. Get reef crystals because it's cheap or another salt that says its for a reef. Mantis need iodine in order to molt and survive for any long period of time. Most not if all salts meant for a reef will have more then enough iodine in it so don't worry about that. Make sure you keep a close eye on the water level in the tank and top off the tank with fresh RO/DI water. Flucating salinity will stress a mantis and drastically shorten it's life.
2: large HOB filter with filter floss and chemipure in it
3: Largest sized substrate you can find and completely cover the bottom doesn't have to be deep just enough to cover the bottom. Mine is litterally made up of shells and other large pieces of stuff. If you go with a small mantis you could do whatever sized substrate you want.
4: Rock, enough to build a nice sized cave proportional to the size of the mantis with multiple outlets. You can start with dry base rock to cut costs and make is live rock. If you wanna speed up the cycling process buy a .5-1lbs piece of cycled live rock and throw it in there to seed your dry rock. Or go with all live rock it's your choice. Either way the tank is going to cycle and has to mature 3 months before you can have a mantis.
5: Lights, keep it simple and cheap you need just enough light to light the tank for viewing and create a day and night cycle. Get a cheap LED
Amazon light it'll be more then enough. If you put a light meant for coral over the tank the mantis is more then likely going to hide when it's on which means you'll very rarely see him. This is do to the fact because their eyes are sensitive.
Optimal equipment that'll make life easier but not necessary -
1: Auto Top OFF (ATO) and toms aqualifter pump with mounting bracket to accompanie the ATO.
2: Power head(s)/wave maker(s). It'll help keep crap (detritus) from settling on the sand which in return will help nitrate and phosphate levels down. A good cheap one to get would be a jebao wp-10 with controller or 2 wp-10's with duel controller. Both can be found on eBay.
3: HOB skimmer. Keeps nitrates and phosphates from being produced.
Side notes* -
I'm not going to go over how to cycle a new SW tank. There are countless threads on the forum that'll tell you everything you need to know. If you have any questions feel free to ask. Lastly which I can't stress enough KEEP UP ON ROUTINE HUSBANDRY AND WATER CHANGES!!!!! These guys are filthy eaters and will pollute water quickly if left unattended. Do what I just said and you'll have a happy mantis that you can enjoy for years to come.