In addition to the good advice Tullochgorum gave,
I have been Geocaching for a couple years, i did it for about a year with just my phone, later i bought a dedicated GPS device, used it for awhile and then went back to my phone. With the correct app a phone is just fine. I find mine to be accurate to about 10 feet, with the given hints and whatnot in the geocache descriptions i have hid many with people finding them just fine.
I also have had many occasions where when using my phone and a friend using a GPS device, i walked right up to the geocache where as they were a bit off and much slower to find it. May just be luck in that instance but i am confident that a phone will work okay for you.
Also if you are new to the hobby, not much point in dropping a couple hundred dollars to try something you may or may not like. If you do it for a while and feel you would really benefit from a GPS device, then drop the money on one.
I however also like using my phone because i can find the cache and record the find and make any notes or record the picking up of travel bugs right there on the same device rather than having to keep switching back and forth.
Hopefully this helps, and happy caching! Be careful though as it's addictive! Also be sure you are not encroaching on private property in order to get to a cache, unless it is specified that the land owner knows of the cache and is aware people may be looking for it.
I would look into the Cgeo app, it is what i use in addition to a separate compass app that tells me headings and such for puzzle and tricky caches. I use the compass to get a better heading that cgeo as it tends to be slightly more accurate, both were free on an android device.