Even with good tubes in the DV, the circuit has design defects and the power levels sent to the heating elements tends to be (or can be, depending on the batch and what they used during the build) somewhat higher than the ~6volt it should be. This will kill those expensive tubes off much quicker then it should. Plus they're extremely prone to noise coming from the AC used at the heaters. I've rolled through at least $500 of tubes (not counting the factory box of Svetlana 6H13C/6AS7G I own), and just couldn't take it. Set that bugger on a shelf until I build up the ambition to rip its guts out and rebuild it using DC heaters and a proper bypass for the pre-out when using headphones. For anyone considering one, I say check out the xDuoo TA-03S. You get very similar bass extension, great sound, and the 6C19P driver tubes it eats can be had for $2.50-$5.00 in lots of 50, like $15-30 in pairs on ebay, and $50-60 in pairs from reputable vendors. Just don't bother using the built in DAC.
Picture with the last set of tubes I tried on my DV:
If all you want is a taste of the tube, score a pure tube buffer. A simple cathode follower like used in the Yaqin SD-CD1, SD-CD2, and SD-CD3 will do the trick. Those can be had for $100-300 new and used. They'll drop the gain a very very small bit, but inject the tube harmonics leaving your primary amp to do all the real amplification. The main difference between the three is the tube type used. CD1 is a single 6922/6DJ8/6N11 dual triode, CD2 is a pair of 6AK5/5654/6ZH1P/6J1/WE403B sharp cutoff pentodes, and the CD3 is 6SN7/6N8P triodes. All three use insanely simple circuits which are very easy to repair and modify.
A lot of tube lovers right froth over the sound of 6SN7, and you can easily find NOS and current production of them. I'm kinda fond of the 6AK5, while incredibly easy to find and super cheap NOS, none of them are current production.
Example of the CD3:
CD2: You can also get one of the cheap preamps from companies like Nobsound or FX Audio, but they're just as hybrid as this xDuoo amp, and likely with more questionable build quality.
As pure tube amps go on the cheap side, the GenTune APPJ PA1502A I mentioned is almost a giant killer. Can be had for $200-300. By default it uses a 12AU7 at the input, and 6V6 at the output. The power supply in it allows one to roll the 6V6 to a 6L6, which is one of the most popular and widely used power tubes available. All the tubes in it are easily found in both NOS and current production. Plus from my standpoint, it works well with every set of headphones I've tried on it, and a fair number of IEM. It does have few questionable design decisions with regards to the coupling capacitor capacity (0.1u vs 0.22u and 0.47u), so higher Ω cans get a bit less bass extension than they could. Easily fixed if you're handy with an iron, but not offensive enough to make one rage quit the amp if you use it default. ;)
Anything from Schiit is going to be a good choice, they build to last but design to NOT have the major tube sound, typically aiming more for a neutral thing. You'll get some taste, but a lot less than found elsewhere. You'll also likely end up being able to use most all cans and IEMs with their gear.
Edit:
You may also want to consider one of the LOXJIE P20 amps (like has been mentioned many times today). They're dirt cheap hybrid at $99, and have a balanced output. They eat the not current production yet easily found 6N3/5670 tubes, but have a sound signature that is closer to the cold analytical solid state than tube. Also don't play very nicely with low Ω cans, causing some minor frequency shifting on anything lower than ~45Ω.
(Edited)