I recommend the FritzBox 3370 (tech specs here, although in German).
4 Ethernet ports. All are Gigabit Ethernet (1000BASE-T).
Great signal coverage with external antennas. You would have to add external antennas, which is possible without permanent modifications, for example with the Frixtender products. You can add multiple different ones with different characteristics depending on your local situation. (I did not personally use the Friztender items so far, but added a similar aftermarket antenna to a FritzBox, and it works ….)
Dual band wifi. In case your wifi signal strength issues are related to having "too many neighboring wifis" with no locally unused, interference free channel left for you, then you can simply switch from the crowded 802.11b/g/n 2.4 GHz band to the 802.11a 5.0 GHz band. Range (esp. with obstacles) is less due to the higher frequency, but speed at limited range may be way better due to less RF noise.
Supported by OpenWrt. See here.
Internal DSL modem. Not too important, but saves one device. However I am not (yet) sure if OpenWrt supports the internal DSL modem. It does so for some FritzBoxes like the 7130 (see). If not, the LAN1 port of the FritzBox can be used as WAN port and a DSL modem can be connected there (see, in German though).
Great price: 10 EUR. This is a product that did cost 180 EUR new, but the manufacturer support ended (no matter when you're on OpenWWrt anyway) and a lot of these are in the market from subsidized DSL contracts. So you can get lots of these for 10 EUR incl. shipment, for example on ebay.de. (I do not expect any problems with used, older FritzBox devices. One of them (model 7050) at my place is in use since 2005.)
Method of search. I selected AVM FritzBox as a brand that is good quality and usually supplies DSL routers that come subsidized with people's broadband contracts in my area (Germany …), as that makes very cheap prices probable. Then I looked through all FritzBoxes supported by OpenWrt and found the 3370 to be the only dual-band wifi router among them with 4 Ethernet ports and a great price tag.
There are similar FritzBoxes that add an analog phone port but only provide 802.11b/g/n 2.4 GHz wifi and less than 4xGbit Ethernet (FritzBox 7320, 7330, 7360). (No match. Esp. since now that most domestic phone connections are SIP anyway, I'd rather choose a native SIP phone instead of combining it with a FritzBox.) And again others that are the same but without phone and internal DSL modem (FritzBox 4020).
Only the relatively new FritzBox 4040 comes close again. Unlike the 3370, it does not have a DSL modem but an Ethernet WAN port – not an issue, as an external DSL modem can be connected to the WAN port when needed. Adding external antennas is also possible (see). It is however five times more expensive (50 EUR used on ebay.de right now) for basically no extra hardware features over the FritzBox 3370, except for "guest wifi". So my choice is quite clear :-)