What should inside of a brick chimney look like?
The chimney should be uniform no chunks missing. Cleaning with a brush is not difficult but if it has not been inspected by someone that knows what to look for you can be taking risks.  My current home passed inspection when I purchased it and the chimney was not lined with fire brick just flat field rock cemented together. Needless to say it was a huge fire risk and I have removed it. If you need to use it prior to a proper inspection get a chimney brush and extension poles open the damper and close off the opening with a tight fitting card board or something to prevent the falling debris to cover the inside of your home. scrub the soot and cresode use a high quality flashlight and look for missing chunks. Now the fun part cleaning the debris off the top of the damper. We used industrial vacuums with hepa filters to suck up the soot and cresode if you just have a shop vac you might try to find some better filters for it or have it outside the home because the fine soot will make a huge mess with a standard filter. Once the soot and chunks of cresode are cleaned up make sure the damper will close and open with several cycles (occasionally chunks will get stuck and prevent the damper from operating correctly). Same process for a wood burning stove inserts but there should be a pipe (much easier to clean and inspect) make sure to get the correct size brush for a stove and the job can be done in a few minutes once the cap is pulled.