It all depends on the technical requirements of your ISP (and your WAN speed!).
If you're on an ADSL/ ADSL2/ ADSL2+ contract, the modem isn't going to work (Annex A).
For a VDSL/ VDSL2/ VDSL2+vectoring connection, the modem should work - and rj-45 to TAE cables are easy to get (1-2 EUR, so shipping would be the biggest expense).
With the few fibre/ FTTH connections or the various hybrid contracts (supplementing ADSL with LTE), the modem won't be usable.
In general the Linksys WRT-1900ACS should be a decent router, capable of routing WAN speeds up to 1 GBit/s wire-speed, but it does not include an ADSL/ VDSL modem, nor can it provide VoIP/ SIP services (yes, it can obviously pass SIP traffic through to a dedicated SIP phone or SIP pbx, but you can't connect your existing analogue phones or DECT handsets to it). This means you may have to add additional devices for using the phone capabilities of your contract (if so desired).
There are a couple of modem-router devices (the lantiq VRX200/ "VR9" series) supported by OpenWrt (your Netgear DM200 is one of them), but their performance as router is significantly below that of the Linksys WRT-1900ACS (mvebu), even more so if you want to use FXS (phone) capabilities (via chan_lantiq and asterisk) as well. So your strategy of using a dedicated VDSL modem and a discrete router makes sense (especially beyond 50/10 MBit/s), supplemented by SIP capable devices as needed. The BT Home Hub 5 Type A would be one of the most popular examples for an OpenWrt compatible device combining a VDSL2+vectoring capable modem and concurrent dual-band wireless router into one device (it can do up to ~85 MBit/s routing without flow-offloading, around 100-115 MBit/s with flow-offloading enabled, meaning it's sufficient -but borderline- for a 100/40 MBit/s vectoring connection; devices with FXS ports will be limited to around 55-60 MBit/s, as they have to reserve one CPU core for running the voice firmware).
Because the DM200 only supports annex A or annex M, while annex B (older contracts, usually BRAS based) or annex J (newer BNG based contracts) are common in Germany and required for Deutsche Telekom connections. Which ADSL annexes are supported by a given device depends on the implemented analogue hardware (band-) filters soldered in front of the lantiq modem (and communicated to the modem chip via bootstrap resistors); technically it is possible to support annex A and B (and J/ M, etc.) in a single device, but that requires a more complex analogue filter configuration and is rarely done. While your linked data sheet doesn't specify the compatible ADSL annexes, you can find that information in the full user manual (last page/ pg. 107) - and consequently Netgear explicitly markets the modem as incompatible for Germany:
For VDSL/ VDSL2/ VDSL2+vectoring the ADSL bandfilter setup (ADSL annex) doesn't matter, meaning you can use this device as a modem for the various VDSL flavours (up to VDSL2+vectoring/ profile 17a, 100/40 MBit/s; it doesn't support the newer super-vectoring/ profile 35b, with 250/40 MBit/s) in Germany, but not as a modem for the various ADSL standards.
Given that ISDN proliferation was pretty common in Germany, it is one of the very few countries (aside from some selected ISPs in Austria and Switzerland) which standardized on annex B for ADSL (exclusively). Most other countries selected annex A instead, reserving annex B for the few ISDN lines they supported.
Edit: the same applies to the BT Home Hub 5 Type A, which -as an ISP branded device for the UK- is also an annex A/ M device (so not usable for ADSL/ annex B), but it can still shine as a VDSL/ VDSL2/ VDSL2+vectoring capable device in Germany.
Unless you need super-vectoring now (or very, very soon), the referenced lantiq VRX200/ "VR9" devices are just much cheaper (as in ~10-20 EUR on the used market for pretty nice devices). If you're looking for something new, the Netgear DM200 only costs ~45 EUR, compared to 130 EUR for the Draytek Vigor 165. So it really depends on what you need, now.
I in fact still have my AVM FritzBox 7390. But I currently have trouble with it and I suspect it's the internal modem. I lose my DSL sync with the logs saying "PPP handshake timeout" (dt: "Zeitüberschreitung bei der PPP-Aushandlung.") It takes 2-5mins than I have a connection again. This sometimes happens every hour, sometimes not for days. When I was at Vodafone (recently changed to Telekom) I had the same issues with the FritzBox but never with EasyBox.
Side note: I changed ISP because at prime time the speeds were below promised speeds and latency was above 100ms. This problem is gone with Telekom now, btw.
So much for the backstory and why I thought it was time to change something.
TL;DR: I'm pretty sure my old FritzBox is not the modem/bridge I want.
It's VDSL and my contract says that I need "a modem capable using the VDSL-vectoring-interface of Telekom". It's 100Mbit/s down and 40 up.
So as I understand it, I am just missing the right cables to use my Netgear Modem. I don't care for landline at all. Using SIP would have been a nice addition but it's not necessary.
I previously used a TAE to RJ-45 cable from the wall directly to my Router/Modem. But the modem only has an RJ-45 jack for "internet"/Router and an RJ-11, I think, for "VDSL" aka stuff coming from my wall. It included two different splitters with RJ-11 jacks and some plugs and jacks I don't know the names of. https://imgur.com/a/436RJc2
I suppose TAE plug to RJ-11 jack for seconds splitter would work and then an RJ-11 cable to the modem?
You just need to bring the two active wires from the TAE jack into the RJ-11 somehow.
The "DSL" output of a splitter is a straight-through connection from the input. The "Phone" output has a low-pass filter to prevent the DSL signal from being heard on an analog phone. If analog phones are not involved, the line from the phone company can be connected directly to the modem.
Yes, the modem should do VDSL2+vectoring just fine on a Deutsche Telekom MagentaZuhause L contract. Keep in mind that these contracts are 'All-IP' based (no analogue landline, no ISDN, just SIP) and don't require (mustn't use) splitters anymore. The VDSL modem gets connected directly to the first TAE, with nothing inbetween, so you'll need to get a TAE-6F <--> rj11 cable for ADSL/ VDSL (if you don't find anything suitable in your collection). The splitter shown in your picture is a UK-style one for Annex A and wouldn't be usable in Germany at all.
The Fritz!Box 7390 is known to be problematic with VDSL2+vectoring connections, so problems with that don't really surprise me. Once you have your basic internet connectivity working with the dm200 and wrt1900acs, you can use the 7390 as a SIP pbx, SIP ATA and DECT base station though (behind the wrt1900acs, in IPoE mode --> "Anschluss an externes Modem oder Router" && "Vorhandene Internetverbindung mitbenutzen (WLAN Mesh / IP-Client-Modus)", with "Portweiterleitung des Internet-Routers für Telefonie aktiv halten" --> 30s), so exclusively for phone uses behind your new router.
At least currently, there is no modem supporting super-vectoring/ profile 35b available for running OpenWrt, nor are there really any cheap used options. The Draytek Vigor 165 should be fine as plain modem though (I have its non-super-vectoring predecessor, the Vigor 130).