What's the best product for online giving for our donors that will integrate with npsp? (We cannot afford classy)

Take a look at Give Lively.  There is no cost except the Stripe processing fees. 

It's a basic donation/event platform that integrates with NPSP rather well. 

It's not too sophisticated - for instance, they don't have the ability to sync custom fields to Salesforce yet (they keep saying it's on their roadmap, but they have been saying that for years), but, it does what most nonprofits need for basic donation and event pages.