Both of ours are adoptees who had had pretty awful puppyhoods I'm afraid, so can't advise on early training. I have heard that daschunds in general can be quite difficult to toilet train but both of ours fortunately came with steel bladders!
I would say, just from my own experience, that they can be quite nervous and reactive (although obviously my own two had their own particular reasons to be this way) but I would overall recommend a very calm, steady approach. Mine respond very well to a set routine of walks, training, play and rest.
I found the advice on this website (and the books that go with them - scroll down) very helpful here.
Our youngest (not yet two) was VERY vocal when she first arrived as she had been picked up and carried around in a carrier and then neglected, so she tried to communicate vocally like a human, but I gather barking can be a problem with the breed.
Our youngest is also very bright and very chewy if not kept occupied, and also fearful of other dogs when out walking, so would definitely recommend puppy classes and lots of socialisation (as with any other breed).
Also - please note - they may have short legs but daschunds love to walk (ours could go all day) and they love to explore and dig. So do be prepared for lots of walking and for holes in your garden! I don't have the heart to stop them digging as its a very natural behaviour and they love it!
You probably already know about the dangers of ivdd here but it is important to protect them from too much walking up and down stairs and jumping up and down on to sofas etc (ours do the latter but we are making a ramp for them). Also, don't let them get overweight and make sure they have plenty of exercise so their muscles support the back ifyswim. Best get a decent pet insurance plan in place too (if such a thing actually exists!)
Finally, I have found perfect fit harnesses to be really excellent because they come in three different pieces and each piece comes in a range of sizes ifyswim, so you can get the perfect arrangement for your individual dog. The website takes some studying but once you work it out, its fairly straightforward! See what your puppy trainer recommends but the harnesses do allow our dogs to get quite a bit of traction to pull us along so a lead from a collar might be better initially, until you have yours trained not to pull! Not sure!
Be prepared for a "mad half hour" before bed when they go a bit loopy and dash about and roll around
Having said all of the above, it's difficult to generalise because although our two are the same breed, but they have completely different personalities. One is not the brightest (sorry) is quite "reticient" in his personality and fearful/nervous and disdains balls and not that interested in food. The other is very full of herself, loves retrieving, and would eat anything in reach if we let her! Both of them however are very affectionate, love snuggling up with me (or anyone who is around) and with each other and really give back lots of love and loyalty.
Best of luck op and don't hesitate to pm me or post again on here if you need any more info! I can guarantee you won't regret your decision if you go ahead!