This thead has definitions:
http://soft.com.sg/2006/modules.php?name=Forums&file=viewtopic&t=11895. Have a quick read.
It is put as a sticky for obvious reasons!
What it does not explain is a ROMpler. A ROM is a build-in memory of which information is read but not written - (stands for) Read Only Memory. You probably know this from computer jargon. So a ROMpler is a keyboard/module that retrieves sounds it stored in it's ROM. That simple. Almost all keyboards are ROMplers in a sense. A synth, because it can edit and write the sounds, can be classified as one or not. It stores the sound memory in the ROM - so it is a ROMpler. But it also writes - so it is not. Well, it's all semantics. What is absolutely NOT a ROMpler is a sampler, of which memory is loaded into the RAM and not stored, and they don't have a ROM that stores sounds. Switch it off and all the loaded sounds disappears.
For under $1K, things may get difficult. You may want to try Yamaha S03 - scond hand. It's a synth. I don't think editing sounds will matter much to you since you are starting off and your aim is mainly pop. The sounds you are going to use is going to be pretty standard ones.
If you think arranger keyboards suits your budget and the sound is OK, then go ahead. When you say "composing", do you mean sequencing (recording midi tracks)? There is no way you are going to get anything with a build-in sequencer at that price (ie a workstation). So the way to go about it is software. Software sequencers can be relatively cheap - like the lower end Cakewalk. You just need to make sure your keyboard (arranger or whatever) can support 16 channel playback via midi. You'll need a midi interface to connect your keyboard to your PC - which you can get one at about $70-80. Nowadays, most arrangers keyboard is able to play back 16 channel midi. But if you really want an arranger keyboard, go for the Yamaha PSR series. They have more functionality.
If you really want a synth, your options are fewer at that price short of second-hand ones. Bongman our SOFT resource-man will have to help you here, since he knows all the lobangs for second-hand keyboards.
