What kind of stuff do you want to be able to do? I could probably recommend an independent routine for you. That's for sure the way to go in the long-term.
Well that's the million dollar question! Since I'm such a newbie, I don't have a lot of the language around different sorts of training options, so I have a hard time answering that question. But basically, I want the strength training to support my ability to do other real-world things. I want to be able to do a pull-up and some decent push-ups. I want to be able to play on the monkey bars with my son, things like that. And I've been excited about the ways in which the training I've been doing in the gym has made me a better and more confident skiier- I'm sure I'll also see the difference this summer swimming as well.
I have a feeling that kind of answer doesn't help much...
If you had unlimited money I'd send you to Ido Portal, but on a budget and without a coach, you might want to look into Christopher Sommer's Foundation One and Handstand One. These programs are affordable, you can get lots of coaching in the forums if you post form videos, and it is all about bodyweight strength and mobility, very little equipment needed. It should take someone starting from scractch 12-18 months (rough guideline, don't get hung up on it) to master all of the elements in these two modules, at which point you will have your pullups, pushups, handstands, and a lot more. Then there are more advanced modules you can move on to.
Unfortunately I don't know of any free, publicly available programs that I can recommend, mostly because they are either not individualized, or there is no feedback component, which there is through the forums in F1 and H1. In other words, some of the free programs might be good for some people who don't need adjustments and can police their own form, but I find those individuals to be exceedingly rare. As a beginner, you are going to want to invest in doing it properly. Sommer's stuff is not perfect by any means, but it is affordable, coachable, and his students are doing some incredible things.
The free method would be to become an insatiable researcher and spend a few years, in trial and error, learning about strength training and applying it to yourself. This is the long, hard way, but in my opinion, the best way.
Resources:
Ido Portal for all movement and a holistic lifestyle approach that I believe is the best out there.
Pavel Tsatsouline for no BS strength training through bodyweight and kettlebells, usually
Eric Cressey for more traditional strength training
Greg Everett for olympic weightlifting
From there you could easily find the other worthwhile branches.