Adwords is one strategy to get targeted viewers and hopefully subscribers. Like all marketing campaigns, you need to take a long term view. I believe adwords has certainly helped this channel grow. But it needs to run in addition to on-trend very high quality content that viewers are hungry for. That way you get low sub acquisition costs and high earned views.
As for strategies, there are many you can utilize. You can promote the latest video, a playlist, a group of tags, pretty much anything. You can target time frames and geographic areas and interest groups. Depends what you are after! Some channels grow extremely quickly with no adwords by argetting on trend keywords. Others spend a fair amount of $ and after the initial adwords traffic boost, don't have lasting results. Some are able to accelerate their channel growth with the help of adwords. There are as many opinions as there are channels, which is the way with everything in life.
$ wise, as a rough ballpark, these days you should be budgeting $2000-$5000/month for an adwords campaign to have any sort of meaningful channel growth. 2 years ago when we started, $1000-$2000 or so /month was enough. But with platform saturation, it is much harder to breakout. Hence a higher marketing budget.
But as mentioned above, a critical component to success is very high quality, on trend videos, otherwise even the $5000 will likely be wasted and have no long term benefits.