I wouldnt buy that pre made setup.
first off if you are concerned that cops would be looking for people buying hydro gear for nefarious activities what would catch you eye more someone buying a light set or the whole kit and caboodle.
Secondly it is ridiculously easy to put one together. Videos on grow room set up are only 10-15 min long for a reason.
Honestly if you buy a good light set up and follow rosemans bubleponic guide(
https://www.rollitup.org/dwc-bubbleponics/234626-rosemans-diy-bubbleponics-tutorial.html ) you can have a fucking awesome grow in that closet for the total time cost of a weekend. and i am guessing that you will still have to put most of that together yourself anyways , your 4x7x8 space is twice as large as mine which means heat will be less of an issue. Also if you diy your set up you will know it better than if you buy a premade rig because lets face it you cant send off an email to a company saying "I am having problems using your system to grow marijuana", its just not going to happen. yes it will be a bit more work but there are soooo many people who can help you build an awesome system for easily under $500
for a closet all you need to make a good hydro garden
you need to get some black/white poly (or mylar) enough to enclose the closet
you need to get a ballast
a bulb
a cooltube
hoses that fit your cooltube
an inline blower that fits the hose
you then need the stuff for your "hydro tubs"
for your space i think rosemans 5 gal buckets would be cool, but you could go with the rough neck tubs
basicly the stuff you will need is
a resivoir
an air pump
a small water pump
airstones
tubes
a water manifold from a drip irrigation system(sold at every hardware store with garden stuff)
nutes
some fans to keep air moving
and something to get rid of the smell
if you want a super space age grow that would fit into that space easily and yield an ass load look up vertical growing.
you could hang your bulb vertically using the 5 gal buckets to create a circle... that would rock.
any ways, i say save your money build the setup to fit your situation instead of fitting the situation to your setup...