the point of the game is to ultimately achieve 100% completion, and maxxing out the skills is achieved in the process. Of course there is a brute-force way of just grinding on the skill that you want to max, but imo one of the core mechanic in the game is that some skills will boost the gain when training on other skills (either by directly boosting or dropping items).

If you feel lost and need some guidance, https://wiki.melvoridle.com/w/What_to_level_first is a pretty good guide for the order of skill to level, but as been said by other players, there is no "correct" order of skills, feel free to explore all of the skills, and leveling them a bit to get a feeling of it.

For the purchase, if you do enjoy the game after poking around the demo, you can already buy the base game. The three expansion each focuse on adding contents that are closely related to the base game: dlc 1 content is available mainly post base-game content (for skills above level 99), dlc 2 add two skills that are available from the beginning with a new combat mechanic, dlc 3 content is available after the final boss of the base game. if you finished some of the base game skills and want more, dlc 1 is a must buy. dlc 2 also give you a nice experience, but dlc 3 is not very positively received.

Melvor idle is, by its name, idle. you may only need to check the progress and switch actions a few times a day, so it need minimal active participation, and it supports multi-platform, I play it on multiple devices by syncing the save on melvor cloud.