Designing a 2-way passive crossover is in itself a big challenge, a 3-way even more so. Added to this, the quality of components used in a crossover also makes a huge difference to sound quality and can come in quite expensive.
Further you will need measuring equipment to design and fine tune your xo points and also the enclosure.
Unless you are in it for learning and with a passion for DIY, venturing into crossover designing can be tough and frustrating
In this regard, an active crossover is the best way to go, though you will need amplification for each channel.
For a budget start on active, look for used studio grade crossovers which usually have fixed 24db LR slopes.
Some Class D amplifiers like Allo Volt+ amp offer good quality at a competitive price.
I run a full 4-way active system in my car.
I had a 3-way active system in my home as well, but have since gone with a simple passive bookshelf system.
Some active crossovers in the market
1. Studio grade include companies like Behringer, Dbx etc.
2. miniDSP
3. Dayton Audio DSO launched recently
4. Any of the car audio active head units (rate to find nowadays) and DSPs like Mosconi, Hertz, Audison, Zapco, Alpine etc
Another absolutely budget route is going in for software based digital DSP available in JRIver (much more robust and comprehensive)_and Foobar along with a 5.1 (2-way) or 7.1 (3-way) USB soundcard..
You can refer to my "
Active home audio setup with software DSP " on the following page
http://gearheads.in/showthread.php?23517-Home-Audio-Build-up/page6