IMO, any low-cost VPS provider is going to have a poor reputation. I've even had trouble running websites on some of them, as some "endpoint security" products have their IP addresses blacklisted, causing users to get alarming warnings if they try to visit sites hosted there.
You'll run into the same issues with the "free/trial" tiers of bulk email services like Mailgun.
I agree with OP, you pretty much have to at least send your outgoing email via an established, widely-accepted SMTP service provider, or in some other way pay a lot for a "clean" reputation.
I'd still say it depends. I've used memset (www.memset.com) in the UK in the past without issue. They have low end VPS offerings, but they're not as well known as say Linode.
It isn't so easy to categorise such a service by pure ASN, as they also offer dedicated and colocation services, so you might be blocking a licensed 'on prem' exchange box for a local UK council.
You'll run into the same issues with the "free/trial" tiers of bulk email services like Mailgun.
I agree with OP, you pretty much have to at least send your outgoing email via an established, widely-accepted SMTP service provider, or in some other way pay a lot for a "clean" reputation.