I am not an expert, but here are a few tips.
First, re: the budget. $3,500 is a good amount, but if that is a hard cap that you absolutely cannot exceed, consider earmarking about $4-500 for misc stuff, like cables, interconnects, power conditioners, speaker stands, etc. Otherwise, you might end up exceeding the budget.
It is also important to decide tower vs. bookshelf sized speakers for the mains. You mentioned wanting towers, which is fine, but don’t rule out bookshelves. If you really plan to listen to a lot of 2 channel music, then I agree, get towers. If the main use is going to be TV/movies, maybe not. You will definitely be getting a sub, so the low bass extension in towers is not so important. They also have better dynamics and can fill a larger room with sound, but your room is not so big and you will be sitting pretty close, about 8 feet, so you may not need that extra power. Since towers are usually quite a bit more money than bookshelves, you may want to keep that option open and get a higher quality set of bookshelves.
I agree, rear ported may not work great in your setup.
I agree with the above post, SVS subs are great and they really stand behind their product. A good sub is a must for home theater enjoyment. It looks like your room is only 15x10 feet by 7 feet high, so that is a small room by subwoofer standards. I bet the SB12-NSD would do great there. If you call SVS, or their Canadian dealer, they can help you pick the right sub.
As far as receivers, I believe the general consensus is that most modern AVRs can drive most consumer speakers to decent levels unless you either have a huge room or listen at really loud levels. It is really the features and connectivity that separate them. Most people seem to think that getting the best room correction software really helps. The main brands are Denon/Marantz (owned by the same group), Yamaha, Pioneer, and Onkyo. IMO, I would avoid Onkyo. They do tend to be less expensive and featured packed, but there have been quality issues lately and they use the lowest form of Audyssey room correction software(2EQ). Yamaha and Pioneer are both good, but use their own proprietary software (YPAO and MACC respectively). Denon seems to be the way to go, IMO. They are Airplay ready if you use IPad/Phone, and they use the better MultEQ XT version of Audyssey.
2 possible systems:
Both use Denon 1713 ($450) and SVS SB-12-NSD ($650) = $1100
Aperion Intimus 5T towers, 5C center, 4BP surrounds = $1400
Total = $2500
You could even get a 2nd SB12-NSD and have really awesome bass, total $3150
PSB Image T5 towers, C5 center, S5 surrounds=$2300
Now, just as an example, look at Aperion Versus Grand bookshelves, Versus grand center, and Versus surrounds…total = $1900….Much better components than the Intimus line, if you decide to go bookshelves. Add that to the AVR and sub, total=$3000. (One caveat, the Versus Grand bookshelves are rear ported. They may still work, but I would discuss with Aperion before deciding, once you measure how much room they will have to breathe). Anyway, you can at least see how going to bookshelves allows you to "step up" to a better line of speakers. You could even switch the Image T5 towers for the Imagine B bookshelves, as another example.