In addition to the advice above, probably the best thing I could suggest would be to concentrate on providing maps (of whatever sort) for a relatively small area initially. You can look at the data sizes at http://download.geofabrik.de/ to get an idea of how much OSM data there is in a certain area. For raster map tiles, a fairly run on the mill desktop PC or equivalent virtual server can handle http://download.geofabrik.de/europe/great-britain.html (which is 1GB of .osm.pbf file). For offline maps, I’m not sure about the Mapbox GL option but for OsmAnd’s .obf format it takes me a couple of minutes to process http://download.geofabrik.de/europe/great-britain/england/north-yorkshire.html (38MB of .osm.pbf).
Getting cycle routing “right” for a particular type of cyclist could be challenging - I suspect there’s quite a lot of “secret sauce” involved behind sites such as https://cycle.travel/ and other similar sites (taking into account non-OSM data such as climbs, traffic frequency, urban / rural etc.). Some cyclists just want to get there quickly, some are going for a scenic tour, some just pootling about with the family.
For a university project I’d make sure at the outset that you’ve said up-front what you’re planning to deliver and that you don’t “over promise” - you’ll obviously encounter setbacks on the way through and how you deal with those will be considered when the project is evaluated at the end.