You have to distinguish between three different functionalities:
- xDSL modem
- VoIP/ SIP 'landline' phone
AVM's Fritz!Box line is popular for providing all three features in a single device, doing a bit of everything, without excelling in any of these. Finding OpenWrt supported devices that can provide all of these features in a single device is difficult, so it's typically easier to distribute the functions over different devices - each of them selected to be good at it. While 1&1 might only want to provide phone support for their blessed AVM devices, the law in Germany (Endgerätefreiheit) guarantees that you can provide your own (including running on OpenWrt), as long as it matches the network requirements of your ISP - so you'd be fine using an OpenWrt router.
First of all you need to find out what kind of internet connection you're getting:
- VDSL2+vectoring (profile 17b), marketed up to 100/40 MBit/s
- VDSL2+super-vectoring (profile 35b), marketed up to 250/40 MBit/s
- ftth (with an ethernet cable between ONT and router)
- fttb (using xDSL/ g.fast over old phone lines to connect the individual apartments to the ONT in the basement)
With 1&1 and O² 'mostly' being DTAG resellers, that would suggest VDSL (still, you need to confirm this) - leaving you the question between plain vectoring (profile 17b) or super-vectoring (profile 35b), taking a look at DTAGs Breitbandkarte might help clearing up that question, if your whole neighbourhood (the area surrounding DTAG's grey outdoor cabinets/ DSLAM) is limited to 100/40 MBit/s at most, chances are that your cable segment only uses plain vectoring (profile 17b). While every super-vectoring modem can easily do plain vectoring as well, plain vectoring VDSL2 modems are basically disposable on the second hand market (including some options which can run OpenWrt); modern super-vectoring capable modems however would max out your budget alone.
For plain vectoring, profile 17b up to 100/40, quite a few VRX2xx/ vr9 devices running OpenWrt could be an option as mere modem, including the 'top end' of its class, the https://openwrt.org/toh/bt/homehub_v5a (initial flashing is not quite for the faint of heart, but there are sellers offering pre-flashed second hand devices; consider shipping fees and import duties - still, it's a good device), but any device whose OEM firmware supports bridged modem operations (PPPoE pass-through) would be an options as well (e.g. Telekom Speedport Entry 2, Draytek Vigor 130b or newer, several ZyXEL xDSL (business) modems, Netgear DM200, …). These would start around 5-35 EUR on the used markets and cover the modem side.
If you need super-vectoring, take a look at the Draytek vigor 167 (166, 165) or super-vectoring capable ZyXEL VDSL modem.
For the phone side, you'll need SIP capable devices - either an SIP pbx/ ATA (e.g. Grandstream HT801/ HT802, Cisco ATA 192, …), a SIP based DECT base (e.g. Gigaset N510 IP pro, …), dedicated SIP desk phone (e.g. Grandstream GXP1610/ 1620, Snom, Cisco, etc.) or a (low-end/ cheap) vendor supported AVM Fritz!Box (e.g. the non-AX 7530 would be sufficient, to be used exclusively for VoIP, behind your OpenWrt router). Depending on what you need/ want (if at all), expect around 30-50 EUR (second hand).
Leaving you with the more generic question of getting a good OpenWrt supported router. As mentioned before, the https://openwrt.org/toh/bt/homehub_v5a is the best option if you want to get xDSL modem (profile 17b) and wireless router in a single device, but the lantiq VRX2xx SOC is a bit marginal in terms of perfomance towards the maximum speeds (100/40), while you can handle it with software flow-offloading enabled, this might not be the best long term option. Alternatives would be ath79 (I wouldn't quite buy these new in 2022, but they are still fast enough to cover 100/40 MBit/s), mt7621, ipq40xx, ipq806x, mt7622bv. Plenty of good options ranging from 802.11ac to 802.11ax and roughly spanning ~40-150 EUR new/ delivered.
For 250/40 MBit/s ath79 is losing track and I personally would skip mt7621 in favour of its newer competitors.
For ftth/ fttb (and highend cable contracts) you might want to read So you have 500Mbps-1Gbps fiber and need a router READ THIS FIRST, although -depending on the details- ipq806x, mt7622, and maybe soon ipq807x might also play ball.
A technology switch can look overwhelming at first, especially as ISPs and device manufacturers usually aren't very clear and specific about the important details and considering that you may need a day-one-solution™ before being able to tinker a little more. But there are quite a few decent OpenWrt supported options for either of these WAN connections, just be aware that the higher your WAN speed (and additional requirements), the higher end/ more expensive your hardware needs to get.