Hey Dan,
First of all... does your $1500 budget include an amp? Most "good" keyboards do not have built-in speaker systems like Casio has. (of course, that's a very good thing, seeing as most built-in systems are junk anyway)
Ok... for now, I'm gonna assume that the $1500 is for keyboard alone and you're gonna use a home stereo or headphones for right now.
The first keyboard I would recommend is the Yamaha S-80. It's probably the best bang-for-the-buck keyboard you will EVER find. The usual selling price for the S-80 is about $1400-1600; I've seen it priced at both ends of this range... so if you end up deciding on this board (or any other for that matter), don't just buy it at the first price you're quoted.... shop around a bit.
Here's the rundown of the S-80:
It is a full-size, fully-weighted, 88-key synthesizer. The feel of the keys is really, really good.... very close to an acoustic piano. The sounds are great, but in relatively short supply when compared to comparable boards, such as the Roland XV-88, (these comparable boards are usually priced about $500-1000 higher though). There are 256 preset sounds, covering nearly all categories. The sounds themselves are of really high quality, acoustic and electric piano sounds are a particular high point. If you're looking for mostly these type of sounds, you'll be more than satisfied with the S-80.
The S-80 is also expandable. Yamaha has quite a few expansion boards, most of which also add more polyphony in addition to the new set of sounds. One particularly cool expansion board is the Vocal Harmonizer board. It allows you to plug in a microphone to the back of the S-80, and then the keyboard will add harmonies to your voice based on what chord you're playing. VERY COOL!
A couple other keyboards that you should at least look at:
Alesis QS8.1 - Another 88-key, fully-weigthed synth. This board is very similar to the S-80 and comes with a slightly smaller price tag. I think it usually sells for about $1300. The 8.1's soundset is a little bigger than the S-80's.... but it's not quite as nice. I've messed around a little bit with the QS8.1, and although it IS a good board and has some good sounds; I think the couple hundred dollars more for the S-80 is well worth it.
Roland RS-9 - This board is possibly even more of a value than the S-80 is. The RS-9 sells for only about $1000. It is Roland's newest 88-key synthesizer. Most of it's soundset was derived from the sounds of the XV-series synths. (I play a Roland XV-88, and the sounds are incredible... the RS-9 doesn't fall too far behind.) It's got some great sounds, and a pretty decent feeling set of keys (88-key, semi-weighted I believe). If your budget is on the LOW side of the $1400-1600 range (and you still need to buy an amp with that)... you might want to look into this board.
Korg Triton LE, 76-key version - If you're familiar with keyboards at all, you'll probably instantly recognize the Triton name. This board is a newer, more budget-friendly version of the industry-standard Triton. The 76-key version sells for $1500. Now, I know you said you wanted a full-size board (which I assume meant 88 keys)... but I think this one deserves at least a look. The main thing that sets this board apart from the others is that it has a full-blown sequencer. If you want to record music directly on the keyboard itself without having to hook-up to a computer... you will want an onboard sequencer. Neither the S-80, QS8.1, or RS-9 have one. Another thing that is quite impressive (if you're at all familiar with keyboards), is that this newer version of Korg's flagship has the same high-quality sounds as the regular Triton. I recently messed around with the 61-key LE at Guitar Center and found that it was quite a nice board indeed. If a sequencer is more important to you than a really good full set of keys... check this one out.
Ok... I hope this helps get you started. My best advice would be to go to your local music store (preferably Guitar Center

) and play as many boards as you can. Trust your hands and your ears and keep track of which boards you like and which boards you don't like.
Let me ask you a few questions so I'll have a little more to go on next time you reply:
Do you want to get an amp? If so, will this fall into the $1500 budget??
Can you stretch your budget at all? If so, by how much??
Do you want/need an onboard sequencer?
What styles of music are you gonna be playing with this board? What kinds of sounds are you most interested in?
Well... hope this helps.
P.S. I'd also recommend checking reviews on all of these boards (and any others you might be interested in) at
www.harmonycental.com and
www.sonicstate.com (go to the SynthSite tab at SonicState). If you want a good look at some of the specs of these boards and what kind of prices you'll probably be paying... check out
www.musiciansfriend.com www.zzounds.com and
www.americanmusical.com