OK, As Chris said, I have both, and if asked, couldn't do without either one. Why? The press is my "precision", and the air hammer is my "speed".
Each excels at different tasks, and each works hot steel differently. A press forges from the inside out....meaning that the interior of whatever your pressing, moves/forges the most, while the exterior moves/forges the least.
A hammer works steel just the opposite.... from the outside in.... meaning that hammer dies move/forge the exterior the most, and the interior is forged/moved the least. Its all about heat.... press dies suck the surface heat out of anything your working on....so the exterior simply doesn't move as much as the interior. With a hammer, heat is actually generated by the strike of the dies....this can be proven by taking a 1/2" piece of round or square and under drawing dies, hammer it cold. With a 1/2 dozen of so blows, the steel will start to turn red hot, and quickly there after into orange.
OK, all that being said..... Neighbors and noise consideration?? A press. Very precise at what it does, yet slow compared to a hammer.
IF noise/neighbors are not a consideration....based on what you said you'd be doing..... a hammer all the way...with the exception of San-Mai.....I find if far easier to keep a San-Mail core centered using the precision of the press. With the hammer, I'm constantaly chasing the core back and forth, simply because of the way a hammer works the steel.....from the outside in.
Right now, the Anyang is arguably your best choice. (especially if you can drive to Texas and pick it up yourself....that will save you a huge wad a cash.)
Here's the thing with these smaller hammers ....you mentioned combo dies.....for all but the smallest of blades and/or billets...... IMO, combo dies a waste. I tried using them way back when I was running 25 & 50lb Little giants in the shop, and again when I purchased my Say-Mal 110lb air hammer...... IF you buy a hammer....buy at least two sets of dies with it.....one full flat, and the other mild drawing. With those two sets of dies, you will be able to do everything you mentioned and more.
With a press, I generally recommend at least a 20 ton, and prefer more. With a hammer, you'd be more than happy with the 55lb Anyang.