I have really though of this but what i can build for 600-800 will be far better/usable to a M1 with 8GB. But for anyone reading this post this is something you should be considering. There is a gamble in making an intel based computer for a company moving away from intel.
As far as I can tell the 10gen I7 is only slightly more powerful than the M1 in Multi Core, While the I5 is not as powerful. In the single core it looks to me like the Mac mini is winning. From a GPU perspective the M1 kicks the crap out of the intel IGPU. But the M1 SOC also has Neural engine that helps with video processing, and while 8 gigs of memory seems like a low number it utilization is much better on the M1 as the threw put is much higher allowing 8 gigs to be much more effective. The advantage with the intel build is you can get more memory later and the ability to add a more powerful GPU if needed at a later date.
I am not sure if you are in the US or another country but if you are in the US you can get a student discount and get the upgraded version with 16gigs of memory for $829. From your description of how you use your computer the M1 sounds to me like a Far better choice now and into the future. Also a lot of people fail to calculate their time into the endeavor, if we take just minimum wage of the state of CA $15/hr soon to be $22/hr for fast food workers it takes you 6 hours to get everything put together and up and running you have added another $100 /$132 into the cost.
Let's not forget the possible frustration! There are a lot of factors to consider but at your budget price point and your stated useage I say the M1 is the clear winner. As
@Bustycat noted above we might see a new Mac mini next month that could be even more powerful.
I personally have not upgrade to a new Mac with SOC because the top level M1 Ultra chip Studio is hugely expensive and my rendering software has not been ported to run on Apple silicon just yet... It is possible it never will be so for now I am biding my time.