There's lots of ways to go about finding out what's wrong with your Tele Radix39, and although there are more qualified techs here, I'll tell you what I've learned.
The old adage is; if the radio is working (like yours) hum indicates capacitor failure and poor gain (volume) or reception often indicates weak or failing tubes. That is JUST a general rule of thumb, and by no means the final answer, but you've got to start somewhere. The poor bass response on your radio sounds like a reception issue to me, but it could be anything.
That said, I'd begin by carefully pulling the chassis, check the tubes and check for leaking capacitors. Not really knowing what's inside your Telefunken (I do Zenith mainly) when I get a radio in, I'll check the easy to spot paper caps. If they're sticky, they're bad, but even looking normal they can still be bad, and many folks just change them all while the radio is apart. I've been doing this, I check the value (if marked) and replace with a new one, one by one, so I don't get mixed up. Many sets have a large, stacked (or linked) selection of shielded capacitors on top with the tubes, and you'll need a schematic to check the total value.
List your tube selection and order from either
www.tubedepot.com (who I found on this site) or the excellent folks at AES:
http://www.tubesandmore.com. The site is excellent. Cost? That's up to you to find out...I still have radios apart I need to fix! Expect anywhere from $3.00 all the way to $15-20.00 for the big output jobs.
Dust the chassis, clean the tube pins (and the socket!) and try it again. Surf the web for speakers or a suitable crossover if needed. That's about all I know to say, but there are Telefunken owners in this group that'll probably have better suggestions or leads. Reception is a tricky issue; I've strung yards of cord to no avail, but did finally put together a pretty nice antenna, using the old TV pole the previous owner of my house installed in a cement base. I can pick up AM stations in the Midwest and Southeast with my H-845 after dark very clearly.
Good luck. I'm sure some of the others will chime in with advice and info-