The Magic Initiate feat states:
Choose a class: bard, cleric, druid, sorcerer, warlock, or wizard. You learn two cantrips of your choice from that class's list.
In addition, choose one 1st level spell from the same list. You learn that spell and can cast it at its lowest level. Once you cast it, you must finish a long rest before you can cast it again using this feat.
Your spellcasting ability for these spells depends on the class you chose: Charisma for bard, sorcerer, or warlock; Wisdom for cleric or druid; or Intelligence for wizard.
I realized that this does not allow you to take spells from the Paladin or Ranger classes (they also do not have cantrips, so perhaps that is the reason). But I was wondering if this change would be imbalancing:
Choose a class: bard, cleric, druid, paladin, ranger, sorcerer, warlock, or wizard. You either learn two cantrips and a 1st level spell or two 1st level spells from that class's list.
You learn any 1st level spells chosen and can cast them at their lowest level. Once you cast one, you must finish a long rest before you can cast the same one again using this feat.
Your spellcasting ability for these spells depends on the class you chose: Charisma for bard, paladin, sorcerer, or warlock; Wisdom for cleric, druid or ranger; or Intelligence for wizard.
This change allows for two new options:
1. You can take an additional 1st level spell instead of the two cantrips.
2. You can choose the Paladin and Ranger classes (getting two 1st level spells).
Best Answer
Balanced, the existing feat is equally good
There are two distinct changes in your house-rule and I will deal with them separately.
Adding Ranger and Paladin as options
There is nothing about the ranger or paladin spells lists that make this inherently unbalanced for this feat. Each has a few unique spells, hunter's mark, hail of thorns, etc.. for the ranger and the smite spells for the paladin. But these are restricted to these spell lists more for thematic reasons than balance concerns as there are similar power spells available on the other spell lists.
Most likely these classes were excluded from the list simply for not being full casters. I would have said it was because of a lack of cantrips adding complexity to the feat, but they are also excluded from the Ritual Caster feat which has no cantrip requirement.
It is important to remember that while I can't see an issue with allowing these spell lists from reading through them, I haven't playtested them. Neither have a spent a great deal of time trying to find a build to exploit this. It is possible there exists a spell on those lists that is utterly broken under certain conditions (though I doubt it or more people would multi-class into these classes).
I recommend allowing this on a playtest basis and, as with all house-rules, be prepared to adjust if things don't work.
Two First Level Spells
My gut feel is that this is fine. At early levels it might be strong but with the way cantrips scale with character level I believe two cantrips are stronger than one 1st level spell. Therefore this option is likely a reduction in the power of this feat, and one that most players should avoid taking.
Additionally, there is no way that this could be overpowered. Two 1st level spells can be obtained through the Ritual Caster feat, though not the free castings. With the way the feat is worded the castings are not spell slots so paladins cannot expend them for uses of Divine Smite. The concentration mechanic prevents any misuse from interacts between potential spell choices.
Similar to the first part I believe this is balanced with the original version of the feat, perhaps even underpowered and shouldn't pose any issues. However as I said, someone could always find a potential loophole I haven't thought of, so you should allow this as a playtest rule and be prepared to make changes.
Conclusion
Both your changes to the feat are fairly minor and in most cases, sub-optimal compared to the original. I can see few situations, other than specific character concepts, to choose your variant options over the original version of the feat. If you assess the balance of a feat based on its most powerful options, your version is identical to the existing one, therefore is balanced.