So, this, in the phots, is the ACTUAL ROOM we are talking about .... Right?
Next, let me ask you this, you have small speakers now, how is that working out for you?
Think of the speakers contained in the typical living room home AV system, they are bigger than the speakers you currently have. To cover a lot of space well, you need reasonable big speakers. But, perhaps not 10" or 12". In your case, you might be able to get buy with two 8" full range speakers in front, and two of the same speakers in back. Eight inch speakers are not huge, but they are not tiny pixie speaker either.
As to the stands I suggested you put the speakers on, they can be sized appropriately for the speakers.
My other suggestion, was to mount somewhat thin speakers, very similar to Center speakers on the size walls. These could be mounted up somewhat high, typically, head height to the average
standing man. Four or preferably six, two or three on each side, might work nicely.
Because of the layout, I don't think one speaker in each of 4 corners is ideal. First, the front speakers are behind the person speaking, and that is likely to cause problem with the microphones.
In the Four or Six center speaker scenario, the only precaution would be to get Center speakers that are NOT Rear Ported. Rear ported won't work because the speakers will need to be right against the walls.
Center speakers don't have exceptional low frequency response, but this is an educational environment, not an entertainment environment, and I think the lack of low frequency response will work in your favor. Plus, you will get some bass boost from being so close to the walls.
You could maybe use speaker similar to what you have, only they have to be a lot better speakers, and NOT mounted in the corners. Instead, whether similar speakers to what you have, or center type speakers, I think one pair should be between 1/4 and 1/3 of the way back from the front row, and the second set should be 1/4 to 1/3 of the way forward from the back row.
Think in terms of the seating or listening area, and not the entire size of the room, and place a pair of speakers along one side at 1/4 of the way down, and the next at 3/4 of the way down from the front. Or, you have to use some judgment, 1/3 of the way back and 2/3 of the way back along side one wall.
In a small room like this, don't make the PA do all the work. The PA should just re-enforce the natural speaking voice of the person giving the lecture. It should simply help his natural voice fill the room, not completely drown it out.
Another alternative would be ceiling speakers. Place similar to what I've already described (1/4, 3/4, or 1/3, 2/3) but place in the ceiling. Again, with small speakers like this, you can't expect them to do all the work. You have to look at them more as supporting or re-enforcing the lectures natural voice. You simply won't have a PA large enough to make it do all the work.
You'll have to have amp sufficient to drive the number of speakers you have in stereo. I don't think surround sound will work well in this environment or situation.
I still say you need a basic mixer, and likely one integrated amp driving the necessary number of basic power amps. In your situation, I don't see the need for massive power amps. Just something basic. PA power amps are much cheap than HiFi power amps, so that should be a problem.
But, which mixer, I'm not sure. Some mixers, as mentioned, have common Stereo AUX inputs. If your video sources (DVD Player) also have analog audio outputs, then it is a simple matter of plugging them together.
Some mixers have a separate channel for the AUX input, Some have these tied to specific mixer channels.
Having seen the room, though I don't know all the details of its use, I would say, maybe one wireless microphone for the standard lecturer. That way he can move around, he is not tied to a lecture stand. Then perhaps a couple of stand mount table top mics, if there is ever any kind of panel discussion going on. I did notice a head table at the front.
Now, all this said, I'm not a professional installer. I'm giving you my best guess as to what will work.
There are also a few makers of flat panel speakers. Bower Wilkin is one. Though I don't know how suitable these are for your purpose or how cheap -
BOWERS AND WILKINS FPM5 B&W FLAT PANEL SPEAKER (EACH) at hifix.co.uk
I'm suspecting these are pushing your budget a bit.
It might be worth taking your photos down to a music/PA store, and seeing what they recommend. I'm sure they will offer you some basic advice and help for free.
I suspect, their advice will be similar to mine.
That's about the best I can do. Though I do wish a few other would chime in with their opinions.
Steve/bluewizard