Take a moment to quantify your long-term air "wants" and try to come up with a requirement for a compressor that will continue to serve you into the future. For example, a hobby-grade plasma cutter from Eastwood specs as much as 7 CFM at 60 PSI ( I don't have a plasma cutter, just looked it up.) Another example, I used to have a Craftsman compressor much like yours (looked the same), I was fine for a air-powered tools until I began to use a die-grinder to strip paint and rust off an old car parts. Then I found I could only "grind" for about 5 minutes until the tank emptied and I had to sit and wait for the Craftsman oilless to refill. I would spend as much time waiting as stripping. Now include the manufacturers spec'd duty cycle on the compressor. Many of then only support about 25% duty cycle.
In my search for a new compressor , about 3 years ago, I wanted roughly 12 CFM at 60 PSI to support a die grinder and medium-small paint guns (NOT HVLP) at very nearly 100% duty cycle. (Stopping to wait for a compressor while painting is death on the paint job.) Then I also wanted a small foot print to fit my shop , and I wanted quiet to save my ears.
Others have already given you good advice on quite piston compressors and brands. Some of those would also have suited my needs, except for small size. I found a scroll compressor that ticked all the boxes.
Combining whisper-quiet operation with high airflow and 100% duty cycle, the Eastwood Elite QST30/60 compressor delivers unmatched performance without unwanted noise.
www.eastwood.com
It cost a bit more, but not a lot more than the high-quality piston compressor with >12 CFM.
By the way speed, CFM, rules here. I also considered using my old craftsman tank as an extra air storage tank. The fatal flaw there is that if your job demands more than the max full-time CFM of the compressor then you will run all your tanks down eventually. It just takes longer with bigger tanks. Then you have to stop and wait, even longer. The big tank or the extra storage tank are fantastic for getting lots of air for a short job, no question. The dryer advice given above is also spot-on. Many example can be found at various forums for build low-cost, effective, dryers. 30 ft of 1/2-inch copper tubing, tilted to pool water at each end, with drain valves at each end is a great start.
EDIT: I just looked. The Eastwood Scroll cost the same or a bit less than some of the 5 HP 80 Gal units linked by previous posters.