What should I look for in a tripod in this context? I am currently using the sigma 100-300 f4 and a canon 5d mark ii but am also considering getting a 150-600mm zoom and the MTO-1000 mirror lens so any tripod I get I want to work with those.
Long focal lengths require good technique. And part of that technique is proper tripod selection, and proper use of the tripod. A primary stabilizer of tripods is mass, and the distribution of it. Simply put, the more mass, the more stable and resistant to vibrations the tripod is. Closely related question: How to stabilize a tripod?
But even adding lots of mass via hang bags, sandbags, etc., to an undersized tripod won't overcome the limitations of a tripod and head combination that just isn't up to the task.
I have heard that a heavy tripod is advisable in this context, is that correct and if so how heavy is heavy?
Yes. Caveat: I wouldn't necessarily place the tripod's weight as the primary metric to consider for a sturdy tripod. For instance, a heavy duty (and very expensive) carbon fiber tripod such as the Gitzo Systematic series or Really Right Stuff Versa Series 3 and 4 at just shy of 3 kg is lighter than the largest big-box retailer video tripods, and probably more stable — at easily 5x the cost.
Overall size, and sturdiness of construction (solid leg locks, whether or not there's a center column, sturdiness of the head) and technique (only extending the legs as much as necessary; extending the fatter leg sections rather than skinny tubes when not at full extension; keeping the center column low; etc.) will do more to stabilize a tripod than simple mass alone.
Looking around the web I found the Genesis A3 tripod that looked promising, am I on the right track with this?
For long-focal length photography, I'd say that tripod is undersized. However, knowing that your focal length is coming from a 3x teleconverter and/or a catadioptric (mirror) lens (which are incredibly light for their focal length) rather than big expensive glass, it could probably be serviceable. As I mentioned before, technique goes a long way. For instance, extending as few legs as possible, and removing the center column to mount the included head directly to the tripod as shown in one of their product photos will provide a fairly sturdy base. Granted, you would be restricted to shooting from a low position, but it would be sturdier than at full extension.
IMO, with that tripod, I think the biggest issue you'll be working against is the ballhead that comes with it. I don't think the ballhead is large enough or sturdy enough for big-glass long focal-length photography. Fortunately, you can always choose to just get a larger ballhead later, or as Xiota suggests, a gimbal head.
See: What tripod heads are ideal to mount a large telephoto or supertelephoto lens on a tripod?