Especially for a beginner, a linear supply is much easier than switched mode. It is also usually lower noise - especially common mode noise is difficult (or expensive) to avoid in switched mode supply. For a commercial product, the combination of switched mode and linear is definitely a good option, alone from saving on the heavy transformer and allowing for PFC.
To save on the power loss one would tend to use at least 2 transformer taps, maybe even 4. This is at least what the cheap Chinese do. For the beginning 2 taps are a good start and that does not need a special transformer, but can use a more normal one with a split output winding (e.g. 2 times 15 V). With a fan, a power loss of 100 W is not that bad.
In a linear regulator the OPs in the regulation loop are usually not working as comparators, but as linear amplifiers. Starting with voltage regulator chips looks easy at first, however it does not really help for a lab supply. These chips are made for a fixed current limit and a well behaved load - whereas a lab supply should be stable with any realistic load. So a voltage regulator is not a first step towards a simple lab supply. The LM317 would be used as a kind of transistor (small and relatively slow) with internal thermal protection.
For the beginning, I would start at lower power to learn. Much of the design is the same, but much less magic smoke escaping if things go bad. I attached a PDF file for a simple lab supply design with a floating regulator. This is about as simple as it can get, if you leave out the optional transformer tap switching. It is probably good for about 1-1.5 A and sold by the Chinese as a 2 A supply.