It sounds like you've thought of light, ventilation, soil, and nutrients. I've done cabinet/tent grows and can offer some advice, but let me first say that what you've outlined will work for you, you may just encounter temp issues. I'll mention number of plants too, but after talking about your cabinet.
In my experiences using fans not designed for the purpose of growing (PCs, squirrel cage, bathroom fans, duct boosters) you don't get the airflow you are expecting and end up wasting your time and money. In my experience putting non-vented HPS hoods in a small space....it gets hot. You have the right idea of having intake and exhaust, I hope your surrounding area is cool or can be made cool during your light cycle so that your intake air is like an air conditioner. Regarding light and heat: with your small space a cool tube is probably the right way to do it. With that you'd run a high power vortex fan, likely 6" and mounted to the top outside of the wardrobe along with the ballast...at this point I'd go with a 400W instead of 250...with the PC fans eliminates the carbon filter option. Either way, you'll need LOTS of airflow, so plan on having a couple clip on oscillating fans. I've done small spaces where I use a high power vortex fan at the bottom, blow in the cabinet, and let all the heat 'smokestack' out the top
Survival blankets, or any very reflective surface, can create hot spots and burn your plants. Flat white paint will provide all the reflection you need and be best for your plants...which will likely be touching your walls, I assume.
I can only talk about my medium and nutrient choices, so make sure you know how yours interact and when to give them before making that choice.
Number of plants...such a question. For me, it's dictated by the registry program or it would be 500, haha. Time to learn buddy, not time to be a master yielder. Give one plant your full attention. I'd get one going under a small pigtail cfl, let her get some leaves built up while the light is weak. Don't over water and give ventilation for stalk strength. Setup your cabinet and make sure your temps are ok (you don't really want to be outside of the 70s if you can help it...I get pissed if I hit 78 and start making adjustments, but that's just me...Have a small veg area setup with low temp CFLs and an oscillating fan...you can even run this 24hours if finding another dedicated dark area is tough for you, it won't hurt the plants. When your girl still has a quite pliable stem and a couple sets of branches, cut the branches off of one side and bend the plant as close to 90 as you can get without breaking it...lol, even if you do, don't freak out, if there's even just one branch left she'll live. Here's the kind of bending I like to do....this started when she was much smaller though
and then it eventually becomes something like this with an even canopy and many sites
(metal coat hangers from wally world make great support/spreading utensils). Note how the branches are essentially clean except for the top cluster of branches? Yep, around here we don't have any use for wispy, leafy bud, that goes straight in the hash bin. Only hearty, thick, top buds allowed in jars or bags under this roof, period. And yes, that one in the lower left is a clone rooting in just a cup of un-ph'd tap water...I didn't believe it either, but it can be done. Message me if you are interested in hearing more about that cloning method, I wrote something up on my experience.
Anyways, the point is this: grow that one seed in your small 24hour veg area until she's big enough for your area, bend her out to get higher yield, but focus on growing quality, not quantity. If all goes well during you first veg, then start another seed after about a month or so. When you transfer your one girl to flower you'll have another behind her...you can even clone her if you are up for it by then. You can introduce another girl to the flower cabinet if you have space and time. putting something new into flower every two or three weeks gives you a harvest every two or three weeks! with a cabinet you probably have room for two, with 250w you really only have room for one with an immaculate canopy though, get the 400 or 600 cool tube and be happy later
If you run two in flower then run one 4 weeks before putting in the second. With a good grow, good genes, and ample veg time figure a worst case scenario of 1 oz per plant...hoping for waaaaaay better, just don't get your hopes up...you'll have an oz to last you a month until number two comes...by then you'll get better, you'll be rockin strong clones, having better plants out of veg, more bud sites with more concentrated buds...damn man, getting excited for you.
Hope this makes up for the lack of posts to views and provides something beneficial...it's all just opinion, you'll do fine with whatever you end up doing. Good Luck!