With your wish list, I suggest looking at the Willsenton R8 (the improved later version) or the Muzishare X7. Both are push-pull AB and will deliver 45WPC in ultralinear mode, enough to power average speakers and will have a headphone jack also. The $400 SET EL34 will not be able to do nearly as much for you. If you go with the Willsenton, you might want to upgrade the tubes to Psvane tubes, they are better. If I were buying now, I would get the Muzishare. I have the Willsenton R8, and it sounds wonderful, especially for the money, but I also did the DIY internal upgrades which adds costs but is exchanging the generic components for high-grade audio components and takes some time and basic soldering to do. (There is a upgrade mod series on YT at "Skunkie Does Electronics"’ channel which documents the process well. I found it worth the cost and trouble.
The cost will be $1400 (AMZ) not $400, though, before tube upgrades.