I've been watching this thread and trying to stay out of it as I know all to well which way it would go; stupid, assinine and criminal.
Now before I come off it as a smart ass know it all let me assure you that I do not know it all, yet. I do however know enough about animals and wildlife; please note my signature line and the fact that I am the owner of said enterprise; to have kept my growing family fed and clothed all these years.
First off, forget you ever heard all of the above. I especially implore you to forget the little bit about the willful admission of a federal felony, it's only a $100,000 fine and ten years of your life.
In light of that the very first thing you need to do is get it in writing the exact laws and regulations regarding the take of furbearers and game animals in your specific state, county and jurisdiction. This and only this is the governing authority for you. Internet experts to the contrary, neither I nor any other not intimately familiar with the statutes of your locale can properly advise you on the best course of action. If you would like I do have a colleague that resdies and operates in your state and he would be my go to guy if I had to advise you, better yet I can forward you his contact info.
What I can do in the meantime is to provide you with details from the states I have operated in and others that I am aware of to give you some idea of what you might expect to find in your own state. Be advised though that your state is quite frankly full of fruits, flakes and nuts that have ill advisedly placed bizarre moratoriums on sound scientific wildlife management practices so what I may describe as the proper, legal and preferred practice in one state may be a capital offense in yours.
For instance my residence state of Georgia specifically prohibits the take of both game, to include furbearers, and non game by any person or entity without licensure in accordance with regulated seasons for doing so. To do so outside of established and regulated seasons also requires the issue of a permit to do so. This is across the board, no exceptions not even for the homeowner or farmer. Your only legal out if you do not possess said license and/or permit is you better be able to show the bite or claw marks on your person that you incured prior to doing the deed.
My home state of Alabama is similar in concept save they do allow a property owner to do as needed though you are expected to abide by approved methods.
Georgia also allows for this out for the property owner as long as the property owner possesses a license which the Dept of Natural Resources will freely provide upon request and a quick course on methodology.
Both of these states allow the property owner the sole discretion of determining cause for action others such as North Carolina have a very specific need for actual physical damage in certain specific monetary amounts to have occured prior to requesting a depredation permit to be issued. This damage must be observed and confirmed by an agent of the state to boot.
Then we get into methods. In your state for instance, along with California and Colorado, roughly 75% of the accepted tools in almost every other state of the union are patently illegal. In one, New Jersey, the mere possession of one of those is a jailable offense. Others, like Massachusetts, make only a few of them criminal.
Specifically I am speaking of traps, footholds, bodygrippers, cages, snares, dogproofs, et al. Even in those states where all of the above are legal for use, as in both of mine, even they have limitations upon size location and species as well as stand offs and set backs. Additionally some states may restrict ancillary equipment such as New York's ban on animal parts; feathers, fur and bone; as lures.
Then we have the age old question of what to do with it once caught. Well back home in the Heart of Dixie as long as I remained within the same watershed and county I could drop the critter anywhere I wanted as long I had the written OK of the landowner. Here in Georgia though to do so is again a crime if the critter in question is a RVS (rabies vector species). To fail to humanely euthanize is a criminal offense. Now if your in Indiana you have options if you prefer not to euthanize, you may release the animal from the trap exactly where you caught it or you may euthanize it.
I won't even go into what to do with it after you done with it as even that varies from locale to locale and season to season.
Have I made my point yet?
Now I can't get away from here without doing the very thing I said I wouldn't.
You have been given decent, but not great, advice about traps as the cage trap in your locale, if legal, will be your go to. Just do not go to harbor freight or tractor supply unless your into catch and release, unintended release. I make my living with my cages and can only recommend the very best www.advancedtrap.com
as I make my living with them and my progeny probably will as well. Now since you obviously are not I can make some recommendations. Your very base level cage trap is going to be the havahart brand that can be procured at the big boxes IF you assemble them with care and lots of reinforcements. This is the very base trap I would ever consider putting on my truck and then only as a backup of last resort. With constant use expect less than six months of service life. As you can tell I don't think much of these traps and the moniker havajunk is an industry catch phrase. Before any of the old and crusty reply this applies to current availability the 1079 and 1081 that made the brand are no more, the numbers remain but the quality does not. The next level of cages is the Safeguard and Tomahawk, the Safeguard was my trap of choice for years with the better Tomahawks being their equal. The Tomahawks have something for every budget from havajunk level to the equal of the Safeguard Pro. These will provide a year or more of service based on model and use.
Now on to the cat issue. I can and have caught raccoons right up in and amongst cats with very little difficulty. It can be done but I shall not share that trick on an open forum, PM me or better yet call if you wish. If dogproofs; coon cuffs, lil griz, alcatraz, egg trap, et al; are permissable in your area then dispense with the cages because dog proofs are even more cat proof than cages and can be made cat proof.
I must address one issue that I usually avoid as it tends to piss people off to be called stupid and criminal but here it is. Every jurisdiction that I am aware of has criminal penalties for take of wildlife with toxicants, ie poisoning wildlife. Also every toxicant; pesticide, herbicide, fungicide, et al; that is legal for purchase either controlled or not has been registered with the federal entity as well as each specific state where available and a major portion of this registration is a very specific labeling of specific accepted uses and very specific guides for such use. Again in every jurisdiction that I am aware of failure to abide by this registration and labeling specifices is a criminal offense.
In other words the Federal Insecticide, Fungicide and Rodenticide Act governs the proper use of chemicals and almost every state has there own version as well for a double whammy of legal idemnity. And that only covers the chemical used every state also has statutes covering wildlife so you might just rack up a few more case numbers per event, call it a three for one deal.
Feel free to call me if I can be of help.