You’ll get a broad range of advice on lathes. It’s up to what you are most comfortable using in my book.
Have you looked at Luc Verhoeven’s site? http://users.skynet.be/fluiten/how.html I think he displays a good, economical, low tech outfit for his shop. You can learn a lot just by surveying the photos of flutemaker’s shops to see what machinery they are using. Many have photos on their sites, if they have a site. Others will have had visitors which have posted photos of the shops on their own social media sites. Google around. You’ll learn a lot.
I am not particularly familiar with the machine market in Germany but we live in a global marketplace these days so I am sure what you have available there in new/used machines is similar to what is available here. There are far fewer makers of machines today than there are brands being offered.
I’ll tell you what I use, not so much as a suggestion but just to give you another data point to help with your decision.
I make whistles (high E to low C) and the occasional keyless flute. I use both a woodworking lathe and a machine lathe. I’ve been at it for about fifteen years now.
My wood lathe is a 10" X 38" size with the typical MT2 spindle and tailstock tapers and a variable speed drive. I use this one mostly for rough turning the square wood billets to round dowels. I have also used it for rough boring but I prefer the machine lathe to do that now and everything else besides. It is the similar to the second lathe you pictured but with a bed extension (also rather similar to the Jet lathe that Chas shows). Yes, it is rather portable. I have it bolted to a heavy/high-mass base which reduces chatter from vibration. It is my general wood working lathe for other projects and it has done yeoman duty for me. Still, I would snap up a 14" x 40" variable speed lathe (Jet, Delta, Grizzly, etc. ) if I run into one though. Look at the boring set up on Geoffrey Ellis’s site if you get a chance. Pretty darned ingenious.
My current machine lathe is a 10" x 22" beast with a 1 HP motor, fixed speeds (managed by belt changes) with a 1" hole through the spindle, MT4 taper. I am sure you will think that the bed is short. But with that spindle I can place the work well into the spindle to do many operations. So the bed length works for me. I am also not a fan of long body sections on flutes or low whistles. I can do everything on this lathe from start to finish to make a keyless flute. And to the point Chas raised, I do have a 1 ton crane to move it around in the shop. Still I am looking to replace this lathe sometime in the future. The ideal lathe for me, based on my experience to this point, would be a variable speed 10" x 36" machine lathe with at least a 1.25" bore through the spindle.
I will mention that I have three other smaller machine lathes that support very discreet tasks in my shop for making whistles. Those aren’t pertinent to spec out here. But it is perhaps worth mentioning that I found the need for these after realizing how much time i was spending changing set-ups on the larger lathe and seeing what variations in repeatability those changes in set-up introduced.
Here’s the advice I would give you. Buy the largest machine lathe that you can both afford and house physically (they are heavy and hard to move around). Buy one with more than twice the bed length you think you need. Tooling arrangements can add to your length requirements. The longer the bed, the better. Buy one with the largest spindle bore you can find. Being able to place your work piece inside the spindle bore can reduce your overall bed length requirements. It can also increase accuracy in some cases. The bigger the bore, the better. Variable speed motors are advisable although we all learn to work with fixed speed drives. Better to buy big and have excess capacity than to not have enough. A friend of mine provides this wise council to me frequently. You can always make small things on big machines. You cannot easily or accurately make big things on small machines. Expect to pay as much for tooling as you do for the lathe (sometimes a bit more).
Most of my instrument making friends locally have vintage lathes (Southbend, Hardinge, etc.). These generally came from the demise of local industrial shops ( and there is no lack of shops closing around here). They can be good bargains and great machines. The downside is that they can also be a headache to get operational, to find tooling, to replace worn or broken parts, etc. etc.. Many of these guys spend as much time working on their machinery as they do on their projects. Having a parts lathe becomes the norm. So I would advise that if you buy vintage make sure the machine is already operational and that it has all the tooling you will need to add on. Spares are a plus if you can get them in the deal. But YMMV. There are machine restoration specialists that provide vintage machines restored to “as new” specs and fitted out, including tooling, if you want to go that route. Expect to pay a premium.
In your neck of the woods you might be able to find a decent second hand EMCO Maximat Super 11CD or Super 13. The Super 10’s had a 20mm bore - small. The Super 11CD has a 26" bed but a large bore (35mm IIRC). The usual Maximat 11 has a 25mm bore. The Super 13 was available with a 35mm bore and a 39" bed. That’d be good. The Emco’s are a good mix of the old and the new. Parts are more readily available too compared to some of the WWII or earlier machines.
You didn’t ask about one of these but a milling machine is a very useful tool. Many makers go without one, as I did for the first ten years I made whistles and flutes. A drill press with an X-Y table will do to start. A mill can do so many things for you. They are useful to making reamers, fixtures and jigs. They are extremely accurate used as a setting-out platform. Once again, tooling is as expensive as the mill. When you need one, you need one.
Oh, and I love gundrills. That set-up alone can be a decent investment.
Hope that helps.
Feadoggie