Panda,
First, welcome to the boards, from NJ,
Regarding the computer question, I'd say "get one", but have tables-and the knowledge thereof- with you as well (along with the depth gauge,timer as suggested by Murdock).
One big advantage of the computer is that you will usually get longer "no deco" bottom times, as the computer monitors N2 absorbtion based on your actual depth, whereas the "table" time limits are based on the premise that you were at your maximum depth for the full dive.
If by "dive trip", you are going to a resort,and planning to dive with a local (there) dive operation, then the computer maye be even more important,in terms of enjoying the dives. Most dive operators will let you "dive the computer"(for time) while others will insist that you follow the table limits. Using my computer, I have been able to get "another dives worth" of time vs. the tables during a 4 dive day.
Regarding the choice of computers- there are many good ones out there, but you need to decide on what capabilities you want in the computer. For example: Nitrox capable (I think this is good)/or not; air integrated/or not; Downloadable to a pc/or not; mounting options : wrist, console, hose, BC.... # of dives saved...etc...and others that probably other replies can mention.
Also, your budget, and future goals in diving should be taken into account. Computers are not exactly low ticket items, and you might want to get "more than you need" now, rather than have to buy a new computer later.(I'm thinking specifically in terms of the nitrox capability)
Regarding the specific computer to purchase-I'm sure you'll get a wide range of replies, so here's mine.
The computers I use are : the Oceanic Data Plus, and as a backup the the Orca Skinny Dipper Mark 2. While I would recommend either as an excellent computer, these are not the latest models -the Mark 2 is more like a computer antique ( I believe Orca is out of business), and the Data Plus,while still available, has been "updated/ replaced" with newer models- but they do what I need them to do. If I had to purchase a computer now, I might go with the Oceanic Data Max Pro Plus-Nitrox capable/ air integrated/ downloadable.
I hope this has been helpful, and if you have any more questions, ask away.
Let us know what you decide to do.
MikeD