The effective but cheap way is zip ties - also known as slip ties or cable ties. They are available in many lengths, but 300 mm long 4.8mm wide is about "normal" and you can get a pack of a thousand for $30-50.
Depending on the clearance above the joists, I'd loop one cable tie around the wood/metal, and then loop a second cable tie through it, ...
If future access is a concern (is your drop ceiling a pain open up?) then I would run conduit. At least for some of it. More work and expense now, but in ten years when you want to replace the cable with something better, you'll be able to just pull it through.
I like using these in my attic, even though they are designed for Romex. I like how they can clip multiple cables in.
Sometimes I replace the nail with a screw for easier installation.
Multi-Cable Staples (20-Pack)
Cat 6 is roughly the same size as its RG-6 coax counterpart. Coax clips can be easily found everywhere and they drive in fairly easy to wood (nail-in or screw varieties). This clip on Amazon even mentions Cat 6.
This answer is from an Australian (licensed cabler) perspective. Based on the fact you have metal conduit and a basement, I'm assuming you're in the US/Canada.
The rules here are definitely open to interpretation, but there are two main clauses from AS/ACIF S008:2006 - clauses 8.1 and 8.6 that apply here (in AU):
Telecommunications cabling must be supported ...
Simple cup hooks will suffice
$5 for a pack of 25.
If screwing into the bottom, then at the first joist, you have two of them about an inch apart, and you face them opposite directions (not like in the photo). That way, to get the cable into them, you have to zig-zag it. This assures the cables will not escape.
Then every couple of joists, you have ...
If you read up on the standards for datacom cabling, you might end up with your head spinning. Those standards are very demanding and detailed. They do make sense for big installations in commercial buildings, hospitals, data centers, etc.
But keep in mind, you'll also find tons of material based on partial understanding of the industry standards, and some ...
For a fixed run, I use ring-type wire ties (they have a ring at one end for a screw to hold them in place) and I would screw them into the framing in this case. They are much less fuss than the plates you screw in and then attach a wire tie to. DO NOT "pull them as tight as you can" or you may damage the cables, particularly at corners.
I usually use a wire stapler with appropriate staples.
They also make plastic cable staples that can be used if you don't want to invest in a wire stapler.
Either will work but the stapler is a lot more convenient.