Hi,
I built something very similar to yours a few years back. My suggestions both for good sound and optimal costs in mind.
1. Between the tweeter and mid-range use passive xover, fairly cost-effective and not too difficult to design
2. Active 2-way using 2by4 MinidspHD, the one channel driving the Tweeter and mid and the other driving the 2 woofers in parallels, this way you can control the frequency response very easily. The sound is very good indeed.
3. The tweeter and mid-range use tube or solid stage to drive them, you don't really lots of power, an EL84 push-pull(not expensive) or even a single-ended tube or prefer solid-state use LM1875 or 3886, all these amps sound very good.
4. The bottom end woofers use a high powered digital amp, so many around and cheap too.
BTW the ALpha 15 is not really a real improvement on the Beta 15. You need to spend more money to buy a better 15 or even 12in woofers. Look at the SB Acoustics 12" or 15" open baffle woofers, I haven't heard them you still need to do more research before buying. For my system my woofers are my weak link, so spend more money on getting high-quality woofers.
Your speakers should sound very good once you finish with them. Huge sound stage, great clarity and openness.
Good luck.