Saltwater requires a lot of work and the right equipment. It is also expensive to maintain. Go talk to one of the experts at your local store so they can show you and your Mom what is required.
I would disagree with saltwater requiring a lot of work and being expensive. It can/will require the amount of money and time you wish to put into it.
The big difference between saltwater and freshwater is salt. Pending the size of the tank, a single large box of salt can last you a long time. I will also add, you would want to include a refractometer so you can measure salt levels; which will cost an additional $15-25.
Most equipment is optional, but most others will agree that a good "protein skimmer" is well worth its value (anywhere from $100-500). Also, a heater is necessity. And many will agree that choosing a "reef ready" (aka "drilled") tank has a lot of value, despite its extra cost. This allows you to store a sump underneath the display area. Sumps can be expensive, but dont have to be. My first 75g tank had a 5 gallon bucket for a sump, before i upgraded to a large plastic storage tote. But after a while, you will likely upgrade to an acrylic sump.
The biggest step will be if you want corals, which will require special lights. These can be surprisingly expensive. But most will recommend avoiding starting a brand new tank with corals. If you want them, add them after 1-3 months.
If you decide to go through with it, the first big question is "how large of a tank do you want?" Id recommend anywhere from 40-120 gallon... unless you want to go bigger, then id say do it! These medium sized tanks will give you fair stability (easier and less stress) and a little room to grow while still potentially satisfying your wishes for a long while. Going smaller often causes many troubles and headaches that result in people abandoning their tanks immediately after starting, or spending significantly more time and money than needed in the beginning.
Oh, and as for fish. Start with just 1 or 2, no more for the first month. Ocellaris or Percula, Clownfish, are excellent beginner fish and highly recommended. As for food, i recommend avoiding pellets or flakes. Instead buy a small pack of frozen food. You can ask the fish store what they recommend, but i like starting with the purple Hikari Mysis Shrimp. Hikari makes a bunch of small ice cube-like packs of frozen fish food. And their mysis shrimp will provide decent nutrition without dirtying up the water.
Lastly, buying a used tank is a great way to save startup money. Just make sure that it holds water and doesn't have any cracks. Note that if a seller is including any live (wet) rock or sand, fish, corals, water, or anything else biological... then you may be saving money but you are also inheriting any of thier problems/diseases/pests. So do so with good inspection and a grain of salt (of which you will have plenty).
Welcome and good luck!