Stability is important. Not so fussed about 3g / 4g or ability to make and recieve calls but wifi is important. It must be able to get to the internet via wifi.
... are you sure a laptop or tablet won't suit your needs?
Don't take this the wrong way, but I think you're very ill-prepared coming here asking for device recommendations. You're vague as to what is important for your device (no reference for "long" battery, "CPU power", etc.), and you're vague as to what you want to do on it (yes, SSH and packages, but can you give a general reason for it?). As others have mentioned, UT is not as similar to Ubuntu Desktop as it comes across you're thinking it is.
But I'm not gonna come in here and not answer your question. In my understanding, you're looking for a pocket PC. Try looking at the F(x)Tec Pro1, the Planet Computer Cosmo Communicator, or the Planet Computer Astro Slide. Only you can be the judge if these devices are good for you. I can't speak for how good UT is on these specific devices. Like Moem said, check the devices page. They'll always be better over time.
A helpful tip: please understand the differences and limitations of UT vs Ubuntu Desktop. Maybe try buying and old and cheap but well supported device to try UT on first, like a Nexus 5 or OnePlus One.
If you find you need a desktop environment but want something that fits in your pocket, all I can do is point you to the GPD Pocket 2 or the One Netbook Onemix2s. I have never used these and can't say anything for them, I just love what they are. Otherwise, look for tablets or laptops. Hope you find something good for what you want.