a quality link is a link that google hates less than all other links.
One of the most powerful ranking factors in google are backlinks, and google hates having its rankings manipulated and so it hates backlinks and backlink builders (ie. all of us, the SEOs and affiliate marketers). So, in an effort to stop us from manipulating the rankings by building links, google devalues every link that's free, easy to get, or both. They would devalue hard to get links, too (and they probably will at some point), but that would mean replacing the backlinks as a ranking factor with something else and I don't think that google has anything better to replace backlinks with at the moment.
That's why over the years article links have been devalued, then bookmarking links have been devalued, then wiki links, and lately web 2.0s links. Most people have easy and free access to such links, so google has to do something to stop us from getting them and since stopping millions of SEOs from building links is almost impossible (yes, even for a giant like google), it's much easier to simply devalue these links. Therefore, whenever google crawls pages and finds links from sources that google knows as being used by affiliate marketers and SEOs it simply devalues them (stops the link juice from flowing into the destination page, ie the page that the link points to). That's why, no matter how many millions of "garbage" (ie. free / easy) links you build you get no value out of them anymore. Sometimes, such links do help a little bit (SEO-wise), but only in very isolated cases and for extremely easy keywords which you could rank for even without those garbage links if you got your on-page SEO right.
With this info in mind, it's easy to see now what quality links means, which is... links that are hard to get, expensive to get, or both (luckily, there are places where you can get quality links for cheaper than what SEO agencies are charging and one of those places is our forum, but there are other places as well)
Now, just because a link is hard to get and / or expensive doesn't mean that it's automatically quality. You do need to pay attention to a few crucial elements of SEO in order to assess the quality of a backlink, and I'm not going to go into details on what constitutes a quality backlink because I don't have the time or the patience at the moment, but in general, a link coming from a site that meets all of these criteria is a quality link:
1) is indexed and ranking in google (since the website already ranks it means that it's trusted by google, therefore it gets google's vote of approval, therefore it will pass link juice over to your site if you manage to get a backlink from such a website)
2) is not seen as a link farm (it doesn't link out to non-popular sites in that particular niche from each and every single one of its pages. There are sites that link out to non-popular sites more than is healthy, and they do get away with it for years until google figures out what's wrong, but it's generally not a good idea to link out to other people's sites from each one of your content pages)
3) is not a web 2.0 site (basically, it's not open for registration and use by others, and not for free anyway. Any website that allows you to sign up for free and post content on your account is usually not worth getting backlinks from because either 1) the backlink is nofollow'd, which means that it doesn't pass link juice to your site, or 2) the site is free to use, therefore it loses some of its value. There are several sites out there - like gumroad, or telegra.ph - that do have some SEO value despite of being web 2.0s technically, but for some reason google has not devalued those yet. So you can safely use them for now, and some of these sites are being made public quite often on the forum, so keep an eye on them and as soon as you find out about one of these sites jump in and create a backlink fast before the site nofollows your links or disables the option to post content. Many of these sites do turn their backs to SEOs, so you need to act quickly when you find such sites)
4) the link is d0follow (this is extremely important because backlinks appended / prepended with the "rel=nofollow" tag do not pass link juice, therefore they won't give you any SEO value, so they won't increase the authority of your domain, which is exactly what you want, that's the whole reason of acquiring backlinks in the first place. So, if you're paying for a "quality" backlink make sure that it's not tagged with the nofollow tag, because if it is tagged like that you're getting ripped off. The only reason you might want to get nofollow links - and you should get them! - is to keep your backlinking profile looking natural, because google will punish you if it only sees d0follow links. So, get a few nofollow links - say, 5-10% of your total backlinks - just for diversity purposes and then move on to more important links, which are the d0follow links)
There might be more criteria.... actually, there is more criteria (such as: type, placement, proximity of other links, relevance of content surrounding the backlink, UR of the page giving you the backlink, number of OBLs on that page, number of RDs of the domain, its DR, etc.) that makes a backlink quality, but I'm not going into more details as you can look stuff like this up in google or on this forum. There's plenty of info on these topics, you just have to want to look it up and to read upon it.
this is not true. Actually, this does not apply to all scenarios. It might be true for some niches and / or sites, but it's definitely not true for all niches and sites. I've had sites ranking within weeks, and others staying in sandbox for over an year, despite of building links to them. It's a per niche / per site basis
you can get links to new website. Just start off slowly so you can stay safe. If you're gonna build 100 backlinks to the same page of a 10 days old site (just example numbers, it doesn't need to be 100 links or 10 days old site) you'll most likely trigger one of google's numerous flags and pattern detection algorithms and might get your site sandboxed for 1-2 years, which I don't think you'll want
Just start off with a few backlinks per month (preferably the good types of backlinks, not the usual web 2.0s and article directories that newbies get because they're free and easy to get), and then increase gradually over several month until you get the rankings you desire. Just make sure to post content regularly all-the-while, as well, otherwise you might raise some red flags. It might not happen, but it's better to be safe
SEO is not exact science, so there's no number that's written in stone. Just get your keyword research properly and, if you manage to do this, you will rank without needing a single backlink (in the beginning anyway)....