Welcome! First...yes, you've got plenty of room for a good crop. I'd make the following suggestions

My flowering room is 28 x 28...it's big enough for four decent sized plants (I use 3.5 gallon square pots that are about 9.5"). If you're going to divide your room into two grow areas (I can't tell from your drawing if you're able to do this, but I'll assume you can), you don't need as much room for vegging...I'd split it 60/40, so that your flower room is about 18" x 30", and your flower room is about 30" x 30". Those are great sizes; you can veg 6-8 plants, and flower up to four plants. Do NOT let your plants get much over 10" or 12" before you start to flower; they're going to double or even triple in size. But don't worry...a 10-12" plant at the begining of flower can give a very good yield. 3 or 4 of them will set you up well.

I think the biggest problem for you is going to be lights. In your veg cabinet, just go with CFLs. They're cheap and easy. Get a four bulb ballast for around $15 at Home Depot. Buy 4 y-socket adaptors for $1.50 each at Wal Mart. Get 4 two packs of 26w 6500k bulbs for $6-$7 each. You've got 200 watts and 15,000 lumens of juice for your 18" x 28" veg room...plenty to do a great job.

I think you *can* grow with the light setup you have but it's marginal. First, T12 fluoros are not very efficient...they put out around 50 lumens per watt. A high output 4 foot T12 will pull 60 watts; a regular bulb will pull 40 watts. So you're talking about 3000 lumens per bulb with HO, and 2000 for regular. T8s are better, but still aren't optimal. With the T8s on the backwall, you're going to get as much or more under canopy light as light on top, and you need light on the canopy. I figure that even with HO bulbs, you're going to have around 12,000 lumens on your canopy...and if your flower area is 28" x 30", that's 5.8 square feet. (And if you're using 4 foot tubes, some of that light is going into the other room. Not worth it.) You've got barely 2,000 lumens per sq. ft. on your canopy, at most. That's just not enough. You're also going to be sucking up energy. 4 high output bulbs will be 240 watts. If you've got 4 T8s to go with it, you'll end up with around 16,000 to 20,000 lumens, depending on if you've got high output bulbs. That's adequate for a grow...but you'll also be pulling 400w, which is a big waste. And the lights won't be hitting in optimal places.

That kind of flower space is perfect for a 250w HPS--I know from experience. It will put out 25,000 lumens. If your ballast is outside, the heat issue could/should be controllable with your ventilation system. If you're really worried about that, I'd think about a T5 system...something like this:

NGW New Wave T5 28 - 2 foot - 8 lamp

Each 24 watt T5 bulb puts out around 2,000 to 2,200 lumens, so you're talking about 16,000-20,000 lumens while pulling under 200w. Add 5,000-8,000 lumens of under canopy lights, and you'd be in good shape.

A bargain alternative is double up what you did in the veg room...use two 4 bulb ballasts with Y sockets, so you've got 16 CFLS. Wal-Mart has 4 packs of Warm white bulbs for $7 bucks; you'd need four. That's about $80 for a 368 watt system putting out 26,400 lumens. CFLs won't give you the under canopy coverage of an HPS, and they aren't as efficient as a T5, but you'll still do well...much better than you would with T12s, IMO.

Bottom line: Don't skimp on lights. It's a drag to have a good space, and get a mediocre or lousy grow because you didn't want to spend $150 to $250, which is really all you need to set up a decent lighting system for your set up. Good luck!