cable recommendation please from router to wall?

... looking to replace the coaxial/bnc cable that runs from router to wall ...

Some detail about your network would be helpful. Why would your router be using coax rather than ethernet?

Sounds like OP has one of those modem/router combo setup. Don't sweat the coax cable.

yes modem/router combo setup from cable company

I guess what I'm trying to understand is why upgrade just the ethernet cable when it appears there are 2 parts to this chain?

is the router to wall portion less meaningful?

Whew!😥 Glad I don’t have to budget for another cable.

The coax cables supplied by internet provider are all one needs, plenty good enough quality.

What about the cable from the junction box to your house? What about the wiring in the modem/router? Probably should change capacitors and other parts too while you're at it. 😐

Lots of variables outside your control?  What's in your walls, splitters, what's outside where the ISP comes into the home.  That being said you cant control those and assuming its all good just make sure to use Cat 6 instead of Cat 5 for best performance.

As long as it is RG-6 solid copper quad shield with a hi-def compression fitting approved by DirecTVfor their installers to use. A store bought cable is likely bogus. Cable techs usually have the good compression fittings, but not always. DirecTV has a high rate of post-op inspection, so their contractors are less likely to skimp on the materials they supply. DirecTV employees are issued quality fittings for free. If you have cable and your installer was a contractor, your installer might have used copper coated aluminum for your coax runs anywhere he knows an inspection won’t happen. They don’t do nearly as many inspections as DirecTv and the fittings really are stupidly expensive. DirecTV also requires all fittings to be changed on preexisting cables used in a system that installer is signing his name to. Same on service calls. Call and ask for your system’s wiring and connectors to be inspected. You should also have an HD barrel present in your cable’s wall plate connector. The visible color inside your barrel ends should be blue. The inner copper wire should not be cut exactly at or below the end of the compression fitting. You should be able to slightly hurt yourself tapping on the business end any coax cable that is not plugged in. If you can tap on the end of it without feeling the wire picking your finger it’s not installed correctly. 

If you want to spend some money to move the ball forward, consider a linear power supply on your router instead of worrying about coax or Ethernet cable.  For a pretty good Ethernet cable at a reasonable price, consider these (link).

Note the seller’s warning about the shielded Cat8 Ethernet cables:

“* This highly double shielded wires may not work with some non-10G equipment which cause “Antenna Effect” bottlenecking network speed (down to less than 100mbps).”

You do not need CAT8 the only cables I use for Ethernet and USB. Very fast shipping and have not been dinged on tariffs (yet) and it is only 10% from the UK anyway. Also agree with @mitch2 on the LPS. Also turn off the Wi-Fi on your router. 

 https://www.hificollective.co.uk/accessories/neotech-neet-1008.html

If you are considering a bit of a cable upgrade I would take a look at WireWorld.  They offer at least three options all of which will meet your needs.  At the expense of getting beat up I actually went with a combination of WireWorld Ethernet cables based on cost and availability on the used market.  I believe the upper end got a little cleaner (more detail). Did not really notice a change in low end.  I replaced my cables between my modem and router, router to music server (SGC i5), server to switch, switch to DAC / Ethernet connection.  Hope this helps.  I would do it again just to take the cables questions off the table. 

While I am a firm believer based on audition that high end component to component connections (phono, USB, interconnect, and speaker cables) and power cables make a substantial improvement in sound quality, I have not found that difference in wall to modem/router connections.  I had a substantial spend ($800x2) on  high end RJ45 and BCN cables for that purpose.  Discussing the subject with the designer of my component and power cables, he said there was no reason for that spend on wall to modem connections/router cables.  A good quality CAT 8 cable will give equivalent performance as long as you avoid hardware store cables.  My high end RJ45 connector had metal housing parts.  Discussing a perceived treble hardness with Aurender and the cable designer, they both said that all plastic housings are recommended, and metal in the connector is not to avoid potential RFI.  Both recommended trying Blue Jeans with all plastic housings.   I did and can verify that they were correct.  Sound quality was equivalent or better in that hardness alleviated and the design, while as not as visually elegant, appears more rugged. The expensive cables now sit in a closet as a backup.  So my recommendation is to not buy hardware grade cables, but also not buy high end cables for wall to router/modem or even router/modem to server/streamer connections.    Go with a moderately low priced but good quality CAT8 cable like Blue Jeans.  This info is based on my experience and recommendations of Aurender and the designer of the component and power cables I use.  You should audition.   Always use your own ears.  If you buy a high end connector and hear benefits, go with it.   If not, spend the money on something else. 

I would suggest looking into fiber internet delivery and get rid of the copper all together.  Many providers are offering this at no cost to customers for the changeover.