Paying bloggers for direct advertisements is a bit of a grey area. It's grey because loads of brands are doing it, but it's such a difficult thing for advertising regulators to monitor.
Check out this guide so you're aware of the guidelines and risks: https://www.ftc.gov/system/files/documents/plain-language/bus41-dot-com-disclosures-information-about-online-advertising.pdf
You should also be aware of the SEO risks to your business. In short, if you get caught paying bloggers to write about your company and those articles contain links to your site, you're at risk of receiving a manual penalty from Google. See this for more: https://support.google.com/webmasters/answer/66356?hl=en
Risks aside, those tactics you noted are fine, and can work great. Depending on your product or service, You might want to consider signing up for a variety of the affiliate networks out there such as ClickBank or Affiliate Window.
Lastly, the best way to get them writing about you is to make them a part of your growth. Find relevant bloggers in your niche and recruit them as your product testers and focus group. If they feel a part of it, and your product or service genuinely enhancing their lives (or the lives of their readers), why wouldn't they write about you?
In terms of the common methods offering incentives such as sponsorship, discount codes and product incentives are common but you need to ensure disclaimer are made in the right way and any links pointing back to your site contain a rel='nofollow' tag in the link code.
For search engine purposes you need to make sure any links coming to the site are stated appropriately with nofollow tags. Google recently provided further guidance on this area shown at https://webmasters.googleblog.com/2016/03/best-practices-for-bloggers-reviewing.html
Also you may want to see if the blog has a suitable disclaimer policy to handle sponsored posts and links. For example http://www.moneysavingexpert.com/site/moneysavingexpert-finance is a very good example of how affiliated links are ethically handled as they state in the section of this page at "We want you to know when links are affiliated..."
Having specific two way guest blogging partnerships may help where you promote other bloggers and then they promote your services.
There are a number of blogger community sites, blog directories and pay for review sites you can use but make sure you have a process in place that will allow you to gain reviews on other websites ethically.
In terms of finding relevant bloggers to write about your services this can be done in a number of ways:
Social influencer research and direct outreach for which some useful tools are:
Buzzstream Discovery - https://idb.buzzstream.com - Social Influencer Discovery
Buzzsumo - https://app.buzzsumo.com/ - Content popularity and social influencer discovery
BuzzBundle - http://www.buzzbundle.com/ - Social Monitoring, Content Alerts and Influenecer Discovery
http://klear.com/free-tools - Find Influencers and analyze any social account across Twitter, Facebook and Instagram
https://www.hashatit.com/ - Find Twitter and Instagram influencers via Hashtag searches
http://followerwonk.com/ - Find and connect with new influencers in your niche
http://www.notey.com/ - Find specific content authors by country and theme
http://content.onalytica.com/ - Find influencers that fit your content
https://www.voilanorbert.com/ - Find an influencers email address
This method will require the most effort to engage in the social community but is likely to provide the best quality results
Note: for all these you need to be very selective here to find the right blogs that will adhere to required standards
Use tools such as www.similarweb.com and Impactana content marketing Toolbar to estimate the readership and social popularity of any specific blog or post on a particular blog as this will help to use the right bloggers that will promote your services to the largest audience.
If you are based in the US or the UK you are more likely to find more suitable blog partners through these but if you are in another country you may want to do a more local search for country specific blog directories.
Blogger and Content communities:
It may be worth participating in a number of blogging communities to help find new prospects such as http://triberr.com/.
Another option may be to joing specific blogger and content groups on sites such as LinkedIn and Google +
It may even be worth checking out whether there are any local blogger meet up groups on meetup.com.
As a professional blogger myself, I get numerous requests every month to promote different services on my blog, so I can comment from my experience on what has proven effective enough to get my attention and support.
I'm going to assume you're aware of any legal issues here, and not comment on that. Just blogger incentives.
1. Find bloggers who want your product
Don't try to get just any blogger to promote your product or service. Instead, get crystal clear on your target audience and find bloggers who fit that profile.
When you reach out, acknowledge aspects of their platform that relate to your product or service―show them you've done your research (this isn't just a cold call/email).
2. Offer a preview or test
Most bloggers are very cautious about sharing products or services with their audience that they don't have experience with, for good reason!
When you start by offering a free account (even if for a limited time) or a massive discount so that a blogger can explore your service themselves, you're more likely to get a fan―not just an advertising outlet.
3. Offer a compelling incentive to promote
Don't worry about paying per click, instead focus on commissions from converted accounts―that way you're forming a partnership with the blogger in question.
The most effective incentives are purely monetary, and typically represent at least a 30% commission or $25 flat fee (depending on your service).
If you have a recurring service, you can even offer a lower commission if the payment actually recurs every month as customers stick around―that kind of offer is rare, and bloggers love it because it means recurring revenue for them.
4. Offer a discount specific for readers of the target blog
Bloggers love to come across looking like a hero. When I tell people to sign up for a hosting account with A Small Orange using promo code "MEESE" for a discount, they love it! And I do too.
As well, when blog readers see a discount or bonus offer attached to a promotion they're more likely to be excited about the promotion rather than see it as an ad.
In short... make it a win-win. I could go on, but I hope that inspires some ideas.
Of course, if you want to dive deeper into this topic, you're welcome to schedule a clarity call 😉