If you're wanting to do this for a hobby, then by all means, dig in, learn and get started.
If on the other hand you would like to have a television that works, and that you might use to watch television, or put to any modern use (i.e. DVD, video games, computer use [including older vintage computers]) then you might want to put this idea behind you.
As kenglish already hinted at, the hardest part of creating a CRT would be creating the CRT. You can actually do this, but you need to create and maintain a vacuum. I am guessing that you probably do not have the resources to do this effectively with anything larger than perhaps, an old used winebottle. And even then, to have something you might use as a television, you need to get a screen included, and deflection logic going properly.
So making the tube yourself is simply right out. A kit would work, if you could find one. I'd question the usability of certain parts, but if the kit is complete with schematics and all, you could source replacements easily. But once you have it completed you will be set with how to get video into it. Likely you will not be able to use much other than simple analogue RF channels. And analogue RF channels are no longer used to broadcast television in the USA, or much anywhere else in the civilised world. You would require the use of a tuner box, and perhaps even a signal converter, to alter the kind of signal that your tuner outputs into a simple RF channel that you can change the channel of your (mostly) homemade TV to. Using other viewing sources (DVD, video game, computer etc.) will still require a signal conversion and you might not be happy with the results. A lot of the work that went into television tech in the past 40 years went towards the inclusion of ICs and various processing logic in order to produce a better, more pleasing picture. Without all of that stuff that has been standard fare in many televisions since the 1970s, televisions like this that you could make will lack all of that and be more subject to all kinds of problems caused by simple background radiation or nearby electrical sources. (Think static, colour purity, weirdness that you don't want to see.)
If you are just looking for an interesting hobbyist project, and since you mentioned making a wooden cabinet yourself (I'm assuming you have the means with a skillsaw, drill, other tools etc.), why not "convert" a recent-ish 90s/2000s television into a wooden case? This would be more easily done and could be completely customised by you (speakers could easily be replaced for new ones, with better positioning, grille, remote placement, etc.) , and because it would already function quite well, you could spend more of your effort into fine tuning the look of the thing, varnishing it up to have the appearance of an antique console. Something like this would still be a lot of work for you, but it would be something more under your control (you get to decide how far is too far, you would actually be "modding" a TV more than making it), more easily accomplished overall, and provide better results with a variety of sources such that you wouldn't mind actually using it daily.