Thinking about an amp.
So you have to be thinking about an amp.
If you are just going to be playing at home, the Egnater Tweaker fifteen tube watt head is really nice. You can mate that to any speaker, even the one in your Line 6, until you can get a better speaker cabinet or an old burned out amp that you can hook up to the speakers in and make a cabinet out of an out of commission amp, two twelve or a good one twelve.
The Tweaker offers a range of sounds capable of making the most of your guitars, both humbucking and single coils. Put a reverb pedal in front of it and it will produce a range of tones that is astounding - all analog, full tube sounds. Everything from clean to overdriven Marshall tone. Same price range area as your CV Sixties.
I like that Sixties by the way. At this moment, aside from my forum surfing, I am playing my CV Fifties that looks the same except for the maple board on mine. Antique sunburst type body finish. I'm playing it thru the clean channel of my Limited Edition Hot Rod Deluxe with a RV-7 reverb pedal between the guitar and amp.
This CV Fifties is an amazing guitar with one of the most beautiful necks on it of any of my guitars. The grain pattern shows a quarter sawn neck and lots of beautiful straight grain patterns with that beautiful blockiness of the grain when looked at closely. I look at the grain patterns on the necks of all guitars that I buy, unless they are painted; and I look for what I see as a nice straight grain with the blockiness in the striations and the quarter sawn look. This look is much more common on more expensive guitars. My G and L Legacy ASAT Classic has this type of neck pattern.
They had one of those Sixties just like yours for sale brand new for 298 by me not too long ago but it sold fast. It was indeed beautiful and sounded great too. They have a CV Fifties tele there now but it is not discounted. The neck on it is a work of art.