CAUTION: Many/most 2-lens kits have a NON-stabilized long lens, and I am pretty sure that the D5300 kit that you are looking at has a NON-stabilized 70-300. You really do NOT want a NON-stabilized long lens. It makes using the long end of the zoom more difficult, because of your body wobble/shake.
You can get a T7i + 18-135 for about $1,000 on Amazon. IMHO, the 18-135 is a better GP lens than the 18-55. With the 18-55 you really need a longer lens, with the 18-135 you can get by without a longer lens for general use.
WHAT wildlife, and from how far? The smaller the wildlife and the further the distance, the longer the lens you need.
As Tim said, if you need a LONG lens, you need to redo your budget. Once you go past 300mm, the lenses get expensive fast.
BTW, the Nikon equivalent to the Canon T7i is the D7200/7500. The D5300 is a step below the T7i.
And you can get a D7200 + 18-140 for about $1,000.