How much does bike price correspond with maintenance needs?
The cheaper bike will probably require you to adjust the brakes and gears plus lube the chain every week or two, and a bike shop to replace the brake pads, chain and cassette every 3-20Mm. For you, that's probably twice in the winter, once in the summer. With rim brakes you will also need new rims/wheels every couple of years, more often if the roads are gritty. But a lot depends on your riding style and the enthusiasm you have for maintenance (hence the 3-20 range). If "lube the chain every week" actually means "the bike shop does that every month or two", they'll probably be putting on a new chain. Count a monthly service at ~$50 and the chain/cassette/pads as $200 and that's $1000/year in maintenance, or $600 if you do the monthly service yourself.

It's important to note that you can skimp on all of this and it just means slightly more expensive fixes and a slightly worse riding experience (gears that skip under power, more resistance from damaged bearings, cables or chains the break, brakes that don't really work). When I was a mechanic I saw bikes where basically everything needed to be replaced, but people were still riding them (and just wanted a puncture fixed or a new basket or something). The bad riding experience means an hour for your 18km commute instead of 40 minutes.

With hub gears and disk brakes, especially with a full chain case, you'll lube the chain every couple of months, put new brake pads in every year or two, and I expect that replacing tyres will become your main dirty maintenance task. With a single-cable hub (Shimano, SRAM) you'll have to adjust the gears after a couple of months (the free service) then again a few months before you need a new gear cable. If you run Marathons or some other puncture-resistant tyre you should wear the tyre out without getting a puncture (a puncture is often the thing that makes you look at the tyre and go "need a new one". I run a Marathon Plus on the rear and have only had one puncture in at least 20Mm. I did get a 3" nail through one though (with no puncture!)

Those numbers are why people often end up with a dedicated commuter bike that costs a fortune up front. New Rohloff Oil every year at $20 compared to a new Shimano hub every three years at $800 makes the $2000 up front cost of a Rohloff seem cheap (a Rohloff will last 100,000 kilometres or more... no-one really knows because there aren't many hubs that have done that distance yet, Rohloff only started about 10 years ago).