If you're replacing a car with a commuting bike then a higher cost becomes much more reasonable. My commuter was nearly 3 times the price of what's now my weekend bike. After the initial outlay the running costs are miniscule next to a car. If I was speccing up an ideal commuter then:-
titanium frame & steel forks
decent 36H handbuilt wheels
SON front dynamo running front and rear light
rear rack, guards, Brooks saddle
either 32 or 35mm tyres with good puncture protection and longevity
would be torn between a SS or Rohloff rear hub or as an outside option a 1x8 setup
The above is a general template and would depend on secure parking facilities, but you can easily reach £3-4k. For me it would all be about minimising weight while maximising protection from mechanicals and maximising ride comfort. When I was still doing my lengthy commute it equated to about 14 hours of saddle time per week. If you multiply that up, taking account of holidays etc, you're still looking at 600 hours a year on one bike.
So I'm fully behind the idea of spending the dosh on the commuter first. After that you can see what you can afford for the weekends.