I am looking to buy a camera for video recording. It would be basically lectures recording and occasional live streaming + recording. Lectures will be of 1 hour typically but might extend to 90 minutes and it will be delivered on blackboard. My budget is $500 - $2000. I don't have much expertise in this field. Any suggestions would be much appreciated.
For recordings (or streaming) of over 29 minutes, a DSLR is not suitable. A DSLR will generally produce better image quality than a similar class mirrorless. However the max recording length of every DSLR is 29 minutes. The max recording length of every mirrorless except for the panasonic GH series is also 29minutes.
So the question becomes do you want to be able to change lenses, use a larger sensor on a modest budget or do you want the simplicity of a all-in-one solution?
I record events lasting up several hours. I simultaneously stream to multiple TVs while I record it to a SD card. I use a Panasonic GH3. This is limited to 1080p recordings. The newer GH4 and GH5 can do 4k but cost more and 4k files are a booger to work with. The GH series all have a line in for a microphone as well as a mini-HDMI out which can go to any device with HDMI in. There are also after market add-ons with higher end inputs for GH series.
I would suggest that this would give you the best overall result while also meeting your criteria including price.
A GH3 is 350-900 (used and new generally in this range depending on age, condition and so on)
Any microphone with a 3.5mm Microphone such as Røde would be great and around 150-400 range.
An extension cord to go from the speaker to the camera will be around $30. If you need a transmitter and receiver to link the speaker and camera allow for around 300.
An oil-damped tilt and pan tripod will be around 100-300. Get as nice and heavy duty a unit as you can afford. The better the tripod the happier you will be. They need some weight and such to damp vibrations.
Which lens depends on the distance to subject. A good one will be 350 to 1200 depending on distance to subject, if you need zoom, etc. I suggest the 45mm f/1.8 by Olympus as a good starting point.