I would recomend the UDOO Family or the Odroid Family (Both came with their own Ubuntu flavor).
Wifi card included
Able to run 24/7 without overheating
If this works 24/7 you could damage the Wifi card; as you need for WiFi, you could instead buy an USB Wifi Module like this or this. The main attraction of the Pi 3 are the Wi-fi and Bluetooth, but in this case maybe is more important to invest in RAM, a best processor and heatsink.
For your budget an excellent investment would be the Odroid XU4
Processor: Samsung Exynos5422 Cortex™-A15 2Ghz and Cortex™-A7 Octa core
CPUs: Mali-T628 MP6(OpenGL ES 3.0/2.0/1.1 and OpenCL 1.1 Full profile)
RAM: 2Gbyte LPDDR3 RAM PoP stacked
USB: 2xUSB 3.0 Host, 1 x USB 2.0 Host
Ethernet: Gigabit Ethernet port
Size: 82 x 58 x 22 mm approx.(including cooling fan) <--- This is a BIG plus.