Should it be is or are?

I was searching online for my first home for about three months, and while there are a variety of homes online, [there isn’t much of] a choice when you don’t have a lot of money. So you filter by cost and there’s only like five [options], so you just choose one of the five," shares the bubbly trainer.

Should it be “there is a variety of homes” instead?

Thanks!

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