Entire place is a paradise for a hiker with wooden and stone paths above lakes, swamps, in front of waterfalls, through forest and into more distant, quieter areas of the protected landscape. One day hike can generally satisfy the need for seeing the most attractive areas if you start early and in combination with established transport options (parks bus and boat); but as your day approach till end, you're getting tired and you're falling in love with Plitvice you'd wish to stay longer - maybe one another day or more! The area is just too stunning to ever get tired of its beauty.
So, beware - if you're planning to go and before you go - one day may not be enough and since the area needs at least one full devoted day, start early (latest at 10 am); best would be if you have accomodation somewhere near in the villages to minimize travelling (plenty of choice in private rooms, hotels or camp sites) to/from park and spend another night after hike in region.
Equipment: If you stick to main paths, basic shoes like sneakers can be sufficient for light and comfortable walk. If you plan more to explore of the paths that are not only by the wooden planks and go through forest or stone, some better hiking shoes are recommended (to minimize pressure on your feet). Remember that if you spend a day here, that can mean walking (and resting) for hours - 5 till 10, which depends on you how much you are walking, how fast, where and if you combine it. There are different paths to choose.
If you stay for few days you can take extended walk into park not only by lakes (seek for information from the tourist office and by thier web site). It is a bear region here and maybe you'll meet him so stay calm if you spot the bear.
Take a bag to where you'll dispose your trash (including used toilet paper or sanitry napkins and food leftovers) and bring enough of water and some meals for the hike. Note that you may not find something what requires special diets here easily and nor everywhere because it's not possible to build restaurants all over the place.
Sticks for nordic walk (it's up to you) is good to have at some spots. Something to cover, sun screen - in summer, sun glasses (anytime with strong sun including winter when coverd by snow).
Some first aid equipment (if your shoes worn you) could be good too, bands and that stuff.
Using small backpack is better than hand bags of course but even everyone seems to know that you're surpised how many people stay good part of a day here 'equipped' rather silly for outdoors (and they're the first one who complain).