Muddy Commute Bike Options

My commute is mostly along an old railway line with some muddy patches then through a farm and onto a road for a couple of miles. I currently use a pretty old heavy hardtail MTB and am looking for something a bit faster and I'd also like to be able to fit a rack and full mudguards.
What are some good, relatively cheap options? I've been looking at gravel bikes (particularly the voodoo limba) but am open to any bikes that would suit the terrain.
What are some good, relatively cheap options? I've been looking at gravel bikes (particularly the voodoo limba) but am open to any bikes that would suit the terrain.
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https://www.decathlon.co.uk/triban-rc520-gravel-id_8504030.html
https://www.planetx.co.uk/i/q/CBPXLDNRIV1/planet-x-london-road-sram-rival1-hrd-road-bike
https://www.planetx.co.uk/i/q/EBPXLDNRDA1M/planet-x-london-road-sram-apex1-road-bike
https://www.rutlandcycling.com/bikes/road-bikes/giant-toughroad-slr-gx-1-2019-aluminium-road-bike-charcoal_462109
https://www.halfords.com/cycling/bikes/adventure-bikes/boardman-cxr-8-9-cyclocross-bike
I love my PX London road as it happens.
For commuting generally, control in mud or traffic I believe flat bars set up are safest with faster reactions braking etc. If you're in a head wind you can still be efficient if you cut down the bar width and fit decent bar ends like the CaneCreek Ergos to get a bit aero'ish!
I use to have a 17 mile commute to work and did it on my CAADX with mechanical disc brakes and it was spot on for my use. Although from my MTB days I do k ow that hydraulics are far better.
The Rival1 version of the bike would make a great commuter, with the right tyres on there.