In my opinion you shouldn't worry too much about those links, although it is very simple to turn white hat: ask those bloggers to apply a rel=nofollow link attribute. As you know, Google is against every manipulative link building technique.
A few years ago Pay per Post type link building techniques were in vogue. You know what happened to them, I suppose.
I don't think Google can tell for sure if someone paid for a post if that certain post is published on a high quality blog. Let's say you know an editor from a certain newspaper, you give him $500 and he'll mention your website in one of his articles? Did you paid for that link? Yes. Can Google determine if that certain link is a paid one? I don't think so.
You should think that Google's algo it's all mathematics, it's all "if" - "than" causal programming.
So, if several spammy bloggers, that write mostly about products, services, giveaways link to you... that is not good and I'd avoid that. Unfortunately, the most starters will do anything for $5-$10 and, to some extent, it's understandable, because they have no revenue.
Also, many bloggers have that Disclosure Policy page, I'd avoid them all, or ask them to use nofollow.
If there are bloggers that own high quality websites, which ain't filled with reviews, maybe I'd pay for a natural looking mentions (can be your plain URL, words like "this website", etc.) but I wouldn't rely 100% on this.
Using nofollow will still deliver you traffic and getting traffic and high quality content maximizes the natural linking probability.
Hope it helps,