I'll have to respectfully disagree with B-bob on this one. This tank, from what I can see, is on the side of higher tech.
What size tank are you going for? That can really impact filter choices. I wouldn't go with undergravel at all, simply because I don't like the premise of them, and HOB, internal, and canister filters are much easier to clean.
With a clean, stream lined tank like that you're probably going to want to use a canister filter, with lily pipes on it to help keep the illusion.
Yes, you're going to need lighting around 6,000k to 7000k. You can use t8 lighting, LED lighting...anything with the proper kelvin rating. Usually, for a streamlined look (coupled with a rimless tank) high tech set ups utilize LED lights as they're thin and sleek. Finnex is a brand a lot of people use. They're not cheap, though.
Fertlizer...generally, with high tech tanks, a lot of people use pressurized Co2 alongside fertilizer. That's not something I'm familiar messing with, though. I'd recommend just sticking to something like Seachem Flourish comprehensive. It doesn't really DO anything to your water, besides add the nutrients plants need. One bottle will last a very long time. People with high tech tanks will often use dry fertilizer, or a mixture of substrate additives which I'm not well educated in.
Plants help ammonia, yes. You still have to cycle though.
I'm not sure that specific plant, but Dwarf Saggitarius and Pygmy Chain Sword are great easy groundcover. The trick is getting it to grow very close together to create the illusion of "grass".
You don't need a mini lawnmower, those plants will always stay relatively small :p Plus if you cut it like grass, often the whole leaf will die, instead of growing back like terrestrial grass. At least in my experience.
If you use D. Sag or Pygmy Chain sword you can get away with cheaper lighting (6,500k Spiral CFLs) but it's not as streamlined/pretty.
For substrate...that's tricky. I wouldn't use large (pea) gravel for that, as you can't really get the same effect. I'd go with sand, personally. I really, really love Flourish Black Sand, but it is expensive and dusty.
That pic is most definitely from a high tech set-up, one that requires a lot of care, dedication, time, and money. It's a lot of work and a lot of research, and can take a while to master balancing high levels of nutrients with high lighting. I'm not saying that it's at all impossible, but to achieve something like in that photograph will take a lot of research on your part, and there will definitely be a learning curve.
This tank is a bit similar, and you can see all the work that goes into making it. https://www.youtube.com/watch?v=COsbWPtDEI0
I don't mean to throw you form this, but just to caution you that there's a lot of work that goes behind this kind of tank.
You can build something similar for cheaper, always, but getting the same look will take much longer as you won't be using near the amount of lighting, fertilizer, pressurized co2, etc.