>When ~ enters the battlefield, choose plains or island. This gains the chosen type.

Alternatively

>When ~ enters the battlefield, choose white or blue. >: Add one mana of the chosen color to your mana pool.

I know what you mean, but the way the rules work with basic lands is that you can't choose a land type and the mana it produces will automatically be associated with it, without extra wording specifying mana it would produce. It's a lot easier to choose a color to produce the color, or to choose a land type and it gains the land type (since basic land types come with innate rules baggage that they tap for their respective color of mana).

Setting syntax aside for a while, this design at the moment obviously has memory issues that should be solved.

It's also dangerously close to being a "strictly better" Island/Plains (having a basic land type is not a factor in that specific scenario - see "This Land is My Land" article for more on that).

For the memory issues, it could be just Flood Plain reprint or, and this is quite an interesting choice, it you could choose to replace it with an Island or Plains you own from outside the game instead of searching for it.

I could also see something like

> When ~ ETBs, you may put a charge counter on it.
> As long as ~ has a charge counter on it, it's a Plains. Otherwise, it's an Island.