Gary is right, the park has fires every season. The biggest one to impact the public was 3 years ago, known as the Cygnet Lake Fire. It was west of Canyon/Canyon Village which is on the east/central part of Yellowstone.
As for the 1998 fire, I worked the fire and it was horrendous, but not devastating. It did not burn the park in the fashion the media portrayed it. More of a checkerboard pattern. As stated before, it was bound to happen with the Forest practices of the previous 100 years. Fire is part of the natural cleansing of the forest. In fact many areas will be difficult to even see where the 88' fire occurred. So much so, the last couple of years many of the information signs about the fire have been removed as they are no longer relevant to what the view is, from those locations.
The question really comes to what time of year you are going. What your plan of things you would like to see and type of overnight you wish to do. Since this is a boondocking forum, there is no boondocking or dispersed camping allowed in Yellowstone. So reservations are going to be needed. I am a boondocker, thus the reason I am in this forum so I am sorry I am not able to give you the particulars.
Your profile shows you have a 25’ Travel Trailer. So I presume that is what you are going to be using. You will have great difficulty getting out to sightsee in the park, unless you leave your trailer at your campsite. If you are going to use hookups, your availability is going to be limited, in the park. One popular and recently reconfigured is at the campground near Fishing Bridge. I have worked, lived and visited Yellowstone National Park for 42 years in a row, but I am not a campground person, so someone is better at giving you recommendations than me. But, I would divide the park in halves. North and then South. Get a campsite down in Grant and one in Madison or Canyon. Spend the north half visiting from a northern Campground and then Southern from the Grant. Don’t forget to visit Grand Teton!
Also, be aware that your solar is not going to be very effective as the campgrounds are in heavy forests and solar production will be limited by that, as well as topography, afternoon showers and cloudy weather depending the time of the summer you will visit. As well as night time temperatures. Be prepared for different weather conditions from May to September, snow/rain/sun/heat.
There is a reason I visit and have worked there, is that it is a place not to be missed in life. But one only see 2% of the park by traveling the roads around the park. See the sites the normal park visitor sees, but search out the real park, away from the typical tourists by Hiking to Shoshone Lake via the DeLacy trail or Fairy Falls or the Water Falls of the Bechler Region of the Pitchstone Plateau.
If you, and anyone else would like my cheat sheet of some of these areas, send me a private message with your email and I will send it to you.
Have a wonderful time, but go and make reservations! You can drive up and hope for a possible opening or cancelation, but if you miss out, it is a long drive to another campground or to one outside the park.
b