I think you need to do some research first on "synthesis"... to get an idea on what a synthesizer can do. Cheez gave a very good introduction to it but you'll need to go deeper. As suggested above, and with a budget such as yours, the Alesis Micron would be a good choice and it does have a built in sequencer. In any case, you can always go software. For workstations, you can't get anything much out of what your budget allows but you can look into second hand though on older models.
I would just like to note that arranger keyboards sounds, in my opinion, is inferior compared to synth unless you go for a really expensive arranger keyboards. To do arrangements, you'll need at least a basic knowledge of music in terms of orchestration (be it band, electronic, orchestral or even ambient and experimental) for anything decent to be realized. Experimenting is one thing, but understanding synthesis will unleash much more power and usage to a synthesizer (in your case I am guessing on ambient synth textures and perhaps some lead melodies, bass lines, etc). No harm knowing more right?
Here's a lead to know more about synthesizers and the world it exist in:
http://www.matrixsynth.com
I agree with Cheez on that you're probably looking for a workstation. If your budget doesn't allow, then you'll have to settle for an arranger keyboard.
Here's a youtube video of a guy playing a Micron with sequences pre-programmed. Abit tacky music but a convenient find on youtube for now that has the sequencer going:
http://www.youtube.com/watch?v=xDU2MHL_5Bg
Here's a little demo on synthesis on a Micron, what he's doing is direct synthesis with no routing and patchworks:
http://www.youtube.com/watch?v=LlZJcu_IRbs&feature=related
http://www.youtube.com/watch?v=f4vItkoMv2Y&feature=related (wait a while and the sounds get pretty interesting)
What it all means is that for a "synthesizer" you "design" your own unique sounds that perhaps we'd never heard before. A "arranger keyboard" let's you play all the sounds that other people are playing. You can achieve a similar synthesizer/workstation environment with a midi keyboard controller + softwares (synths and sequencing softwares)... but that's another school entire though on the same basics. Based on your budget, getting a midi controller + free softwares + basic paid softwares is possible.
have fun...