Note: I run a nonprofit organization and have a different perspective (+ bias!) about donations.
 Generally, I think it's best to begin as you already have by identifying those causes which are most important to you.
 Next, ask yourself if you're interested in pursuing a global / regional / local approach? The local org might focus on issues which matter to you - and it might be directly related to issues in your neighborhood. On the other hand "big" issues like constitutional rights might only be addressed at the national level.
Also, are you looking for a large well-established nonprofit or a small up-start where your money will have a more significant impact? For example a donation of $1,000 to the Red Cross will certainly be welcomed but likely not celebrated. If instead you made that $1,000 donation to a nonprofit running on a shoestring budget of $20,000 a year then you've just increased their budget by 5% - which is definitely cause for celebration!
 By now you should have at least a handful of charities which meet your criteria and can begin validating their effectiveness, transparency, and legal status.
A good place to start is GuideStar ( http://guidestar.org/ ). You will get information on IRS status, financials, mission statements as well as reviews. CharityNavigator ( http://charitynavigator.org/ ) is another great resource and they provide independent ratings of charities. One important distinction though is that CharityNavigator focuses on larger nonprofits (total revenue must be > $1million in the previous fiscal year).
My nonprofit has a listing with CharityNavigator but no rating because we are (much much much) too small. On the other hand at GuideStar we have a "Gold" rating based on the amount of information which we have shared with them. So either of these are great resources but my bias is showing when I lean toward GuideStar.
If for some reason you'd rather not use either of these sites I would suggest that at a minimum that you verify that the nonprofit has a 501(c)(3) status with the IRS and that it has not been revoked. You can search for orgs by name or EIN here: http://apps.irs.gov/app/eos/
For more on charity scams here's some helpful info from the FTC: https://www.consumer.ftc.gov/a...
 Once you have narrowed your list down to 1 or 2 then you can decide if there's a specific funding mechanism which appeals most to you (e.g. PayPal, cash, check, bitcoin). Some donation methods can take 5% (or more!) of the donation off the top before the nonprofit gets the donation.
For example, PayPal charges nonprofits a reduced fee of 2.2% + $0.30 per transaction (details here: https://www.paypal.com/webapps...). Also, BitPay does not charge us anything for bitcoin donations through our site.
Hopefully by going through this you will wind up with at least one charity which meets all of your criteria and can then just confirm their status in the future without going through all of these steps every time. Thank you on behalf of nonprofit organizations everywhere for supporting their efforts!
Of course I have to say something about my nonprofit's work: Jennifer Ann's Group is a nonprofit charity preventing teen dating violence. Our most successful program is producing video games to help young people, parents, and educators learn more about this issue and how to seek help if needed. We have produced 20+ video games through an annual video game design challenge which we have run since 2008. And in fact we will be announcing the winners of this year's contest on June 26th (this Friday).
I speak at conferences about our approach to preventing violence through video games and most recently spoke at GDC earlier this year. My talk is online and free if you're interested: http://www.gdcvault.com/play/1...
Our primary website is: http://jenniferann.org/
Founder and Executive Director, Jennifer Ann's Group