Is the level scaling in might and magic 1 like the level scaling in Oblivion? Does the game punish you for leveling up?

Except for MM2, none of the M&M games have level scaling, only area scaling. MM2 is a mix of level and area scaling.

In MM7, the only place with level scaling is the Arena. World of Xeen has no level scaling whatsoever.

OK, that doesn't sound so bad then. The manual made it sound like the enemies scaled with the characters' levels. I was worried that I would wind up with an oblivion problem of having a sub optimal party and be screwed by leveling up instead of trying to keep my level as low as possible.

Time to grind a little bit :)

I think MM1 also has a bit of level scaling. Not 100% sure though.

I think that MM1 had some mild level scaling. In particular I remember one encounter that was providing me trouble, I levelled up and thought good I can go back and kick some butt, but the group was now twice as big. I also remember exploring an area of wilderness and generally encountering small groups of monsters, then going back at a higher level to grind a little and encountering fairly big groups of monsters.

My impressions was that the level scaling was only about reducing the monster group size if you were a lower level then expected, and that if you increased to the expected level the encounter size would increase to a full size encounter and then not scale any further. I don't think the level scaling changes the types of monsters, just the size of the group.

In contrast MM2 seems to scale many encounters over a very wide range of levels and changes monster types from easy to difficult. The level scaling does seem to be capped, and also set at a level that gaining character levels does make things easier, but only very slowly.

As others have said, MM1 may indeed have some level scaling. But it does NOT punish you for leveling up; quite the opposite. At low level there will be many encounters that are essentially impossible, and gaining levels is the best way to gain strength and be able to handle them. Plus, gaining levels gets you access to much more powerful and useful spells. So gaining levels is highly encouraged.