As Catholics, should we aim to support Catholic/Christian charities? and then the next preference would be non-religious I suppose?
Catholics have no obligation to give to specifically Catholic charities, and are not discouraged from giving to secular charities. How and where you give to the poor is purely a prudential decision, and a matter of personal judgement.
Religious charities, as a whole, tend to have huge problems with lack of transparency, accountability and oversight, and with widespread diversion of funds. Many border on being frauds or scams, and probably most are just that. Catholic charities are no exception: the good apples are outnumbered by the bad ones. Even the Pope’s own personal charity is wracked by scandal and criminal activity at the moment.
Make sure you do your research before you give to any charity. Be extremely careful about giving to charities that find you, rather than the other way around. Guilty until proven innocent is a safe rule. Trust no one until you have thoroughly investigated them. Sadly, religious charities attract criminals because the are not as stringently regulated as secular ones. Even bishops have been known to break the law or play close to the edge when they think no one is watching.
If you want to help the poor, you would get the most bang for your buck by giving to your own parish food bank or other volunteer organization that you can personally keep an eye on, and watch where every penny is going. Earmark your donation for a specific purpose, rather than letting it be entered into a general fund.
Never be afraid to ask for financial statements and reports, and immediately run if they are not provided promptly and with alacrity. Never be afraid to ask question, and never be afraid to say “no” to anyone, even a priest or bishop, if you are not 100% satisfied. Never give large donations without running it past your attorney first.
Also, apropos of your question, do your own research. Put in the effort to make sure that the charity you are giving to is legit and actually does help the poor.