Which CPU Should I choose out of these

With a dedicated graphics card, the integrated graphics is useless apart from Quick Sync. It doesn't look like any of the programs you'll be using rely on Quick Sync, so there's no advantage there. The extra cores of the 3820 and the VT-d support probably make the 3820 the better choice.

I would definitely go with something with more than four cores and four memory slots in your scenario. Running several VMs at the same time and expecting any performance takes plenty of cores and plenty of RAM. The i7-3820 can use up to 8 RAM slots so you have a good amount of memory available, but it is only a quad-core unit. The also quad-core i7-3770 can only handle four RAM modules.

I can think of a few CPUs in your rough price range of $300-400 per CPU that would be better than the i7-3820:

1. The Xeon E5-2620 is a six-core 2.0 GHz (2.5 GHz max Turbo Boost) processor costing right at $400. It will work in the same motherboards as the i7-3820 and also can be used alongside another E5-2620 in a dual-CPU motherboard which any of the i7s cannot. However it is fairly low-clocked compared to the i7-3820 and won't do as well in some of the poorly-threaded desktop applications.
2. The Opteron 6344 is a 12-core 2.6 GHz (3.2 GHz max Turbo) processor costing a little under $400. It has a four-channel memory bus and supports up to 12 RAM modules per socket, although most boards have 8 slots per socket. You can run up to four of these together on one motherboard. This chip is a Piledriver-based part and will be a little slower per clock than the Intel chips. But, the 6344 would be a better performer overall in most tasks than the E5-2620 because it is clocked so much higher and perform better than the i7s in running your VMs due to having three times the number of cores. You also get the full spectrum of virtualization technology and an IOMMU with this chip.
3. Two Opteron 4340s. This will run you about $400 and give you 12 cores clocked at 3.5 GHz (3.8 GHz max Turbo) as well as support for up to 12 memory modules. An ATX dual C32 board costs about what a single LGA2011 board does and you can run any non-Home version of Windows and see both chips. I would probably go this direction if I were you as you are running workstation applications and a real workstation would do better than a desktop.

Having an IGP is meaningless if you intend to use a discrete GPU, with the exception that the IGP-equipped i7-3770 with the Z77 chipset will let you use Intel's built-in video encoder (QuickSync) while using a discrete GPU. The non-IGP parts don't have that little encoder but your discrete GPU likely does in some fashion or another. Personally I don't care for IGP parts since I always use a discrete GPU and the hardware encoders in IGPs and GPUs are very restricted in what codecs and bitrates they support, so I just run all of it on the CPU.