A CNC router will do what you want. I'd think a realistic budget would be around $30k. For that you'll get a 4x8 machine with a vac table, 5HP spindle, steel construction, and an air mister.
Ball park, you'll be able to cut around 60-70ipm in a single pass. Maybe even a bit faster. So on a 8" x 24"
sign, it will take about 2 minutes to cut.
Where you're going to want to invest your money is on hold down. Thin material is by far the worst material to cut on a CNC router. It wants to lift and shift and cause all sorts of problems. You limit this problem by having a really good vacuum table and using the right bits.
One last thing to mention is clean up/sheet changes. You're going to have little shards of aluminum all over the place and the dust collection will do a good but not great job. You can't just pull a sheet off and just slide another one on. That's a fantasy. You have to figure about 5-10 minutes for a sheet change. It's something often over looked.
For that budget you're buying a used machine or building a DIY machine. Neither will likely be designed for what you're doing. You need something a bit heavier and more industrial if you're cutting aluminum all day.