There is a lot of great experience shared on this thread. One of the bottom lines is that everyone's experience is a bit different. However, it helps if the outcomes are clear. You probably want to define the clientele you will be shooting for before doing anything else and identifying the output medium and quality of the video. You say your goal is smooth video - I have seen that on cheap systems with GoPros - but personally I don't like the look of the footage and I don't believe there is enough glass there for good quality and then there is the lens distortion (annoys me to no end - yes you can get different lenses). ..but quality is in the eyes of the clientele.
We use an octocopter because it provides the best redundancy. There have been several times when that has saved the ship - we had a bad ESC and a motor go out. The bad ESC caused erratic flight but we were able to land it fine. When the single motor failed - I couldn't even tell by how the ship behaved in flight. Going the octo path does multiply a lot of the components by 8 so is more expensive.
Like others eluded to there are lots of background expenses that are not seen in the cost of the ship and can quickly add up. However, there are ways to cheap out. For instance, our ocotocopter frame cost - about $20. It is made out of cheap cedar straps from HomeDepot and plywood base plates. The frame was made on a shoe string. This is cheap but it cost in labor and if it ever crashes it will be a total loss. We have mid range electronics in the motors (Avrotor) ESCs (Maytech) and Flight Controller (HoverflyPro). We use a MKPro gimbal with a Canon Vixia G10 Camcorder for video. We get decent footage from it but I know others get smoother results with more expensive equipment.
I think you can get quality footage for much less than $8K but at a price that involves less reliable equipment and more fiddle and experimental time.
I agree with others, start with something that won't kill your budget if it crashes. Invest in a good simulation program to practice on first and spend a couple of months on that before you attempt to fly anything for real. It is possible to go cold turkey but the experienced pilot has to talk novices through the process and the trainer really has to verbalize every motion of the sticks and have the learner follow that with strict obedience. Another option is to use a trainer mode on two transmitters that are daisy chained together with the option of the instructor taking over if the learner gets disoriented.
Probably more information here in this thread than what a novice can take in but maybe come back and research the ideas one at a time to get a better sense for what folks are talking about.