I’ve read that we could send a probe to Alpha Centauri for about $1 trillion.
Its really a matter of scaling up our existing ION propulsion or VASMIR and assembling a “very large” probe in orbit. With a couple of loops between the sun and Saturn to build up a head of steam and the trip could be cut down to a couple of centuries.
The problem is, the government that launches such a probe will almost certainly not be around when it arrives, tens of centuries from now.
There is no known technology that can get a probe to Proxima Centauri (nearest star) in less than 4,300 years (i.e., velocities of >c/1,000). Just doesn't exist; too much mass and energy are required that that amount of delta V.
The fastest spacecraft ever built by man, 'Voyager 1', traveled a mere 15 km/sec (which is c/20,000). If aimed correctly, it would take 'Voyager 1' a mere 8,600 centuries to make the trip.
Also, the communication technology does not exist to send pictures back than any existing radio telescope receiver could receive. It's just too far, and requires too many bits to send even the most rudimentary picture. For more on that, see my post on "Aliens watching 'I Love Lucy'".