Reddit mentions of The TAB Guide to Vacuum Tube Audio: Understanding and Building Tube Amps (TAB Electronics)

You can point-to-point wire it, but you have to mount things to something. A project board might not cut it, but you could get away with it.

The fact that you don't know what goes into a tube amp and why is a red flag to me... I'd really educate yourself first.

Tube amps are expensive before the tubes. Don't even factor them into the cost, they're insignificant compared to the rest of the parts.

Let's assume a decent wattage, about 25 w per channel, push-pull class AB amp. Let me explain just a few of the parts involved.

1. Transformers. Your amp is not going to pull just 50w from the wall. Tube amps are notoriously inefficient, with a lot of energy going to heating the filaments, and even more lost to amplification. Push-pull designs are better, but not perfect. You're going to need a hefty power transformer to reliably and consistently deliver the power. Let's say $70 conservatively.
   
   
2. Rectification. You'd probably stick with a solid-state rectifier for your amp. $25.
   
   
3. AC filter capacitors. Cheap, but a few. $10.
   
   
4. Input coupling caps. If you want nice ones, $20. Otherwise $5.
   
   
5. Misc parts, resistors, capacitors, fuse, jacks etc. $25. This stuff can add up quick.
   
   
6. And now the doozie. Output transformers. The amplified audio signal has to go through these to drop the impedance, otherwise your output impedance is connected to a much lower speaker impedance and it just doesn't work (would overload the tubes, to be specific). The output transformers couple the powered output to the load safely and nicely. The more windings, the lower the impedance matched. And the thing is, the audio signal goes straight through these, so you can't skimp or your amp turns out as crappy as the transformers. Factor in at least $50 each, one per channel, but in most good amps the iron (output transformers) will run $200 or more. The good ones are wound by hand, very accurately. The more carefully constructed the better.
   
   Add it up? $250 bucks. And that's without tubes.
   
   I would recommend a book, and a kit. First the book: Valve Amplifiers by Morgan Jones. It's way expensive but worth every penny if you actually want to know what you're doing. *Edit: This book is cheaper and better for starting out... looks very good in fact.
   
   Next, the kit (you could skip the book and just do the kit, just try to research online too) - The 8LS 8-watt per channel stereo tube amp kit from TubeDepot. It sounds decent, has everything included, and still sells for the bare-bones absolute minimum price of $215. And that's only for an 8W/channel amp! At least it includes tubes, so it's really a pretty decent value, and gets good reviews for sound as well. Here's a slightly simpler design for $189 from the same company.
   
   You can't shortcut your way through this, trust me. Tubes don't amplify on their own, no matter how cheap you find them or how many you have.
   
   And for god's sake, if you don't have experience with high voltage DC, read up on the effects of a 500V shock, because that's exactly what goes through those tubes, right on the contacts. Be careful.
   
   *Edit: Also, for the tube you linked in your OP, that's a 12AU7, which is a fairly low-gain double-triode tube. Usually used for a first stage of a stereo amp or in a preamp. You'd need two of those, one for each channel, plus four main power tubes, which are generally larger and more expensive ($15 minimum per tube). This is because in a push-pull configuration (which is the most efficient available to you, so most likely will be the cheapest way to get a decent wattage) each tube does half the work, and the channels are separate, hence 4 tubes minimum.