I'm surprised that nobody has mentioned that you pretty much HAVE to have a depth gauge, anyway. (The exception would be if your only diving was in a setting where the max depth was so shallow it didn't matter how long you stayed down.) It's kind of hard to find a Bourdon tube depth gauge nowadays, so you're going to be buying something with a battery, and if you're going to do that, you may as well buy something that has computer functions as well. The two commonly purchased bottom timers nowadays (devices that give nothing but depth and time) are both expensive enough that you could easily buy a computer for the same cost.
For the vast majority of recreational dives, tables will be more conservative than a computer, simply because tables (unless you are using something fancy like the PADI wheel) don't give you credit for multi-leveling the dive. They assume you are accumulating nitrogen at the rate that you are doing at the deepest point in your dive, throughout your whole bottom time (which is generally not the case). So they calculate allowable time based on that idea. Computers, on the other hand, are doing an iterative calculation of nitrogen loading, and some even start to give you credit for offloading nitrogen as you shallow up the dive, so your allowable bottom time can be far longer.
When I first learned to dive, I got a computer, and I immediately found myself baffled by some of the shore dives we did. They simply wouldn't fit into the tables -- according to the tables, I was going into deco repeatedly!
Now, I'm one of the folks today who doesn't use a computer any more (as a computer), but it took me quite a while to get there, and I think most new divers are well-served by having something which can keep them from -- through distraction or miscalculation or any other cause -- exceeding their no-deco limits. This is especially true for repetitive dives.
Ascent rate is not that hard to track on your own, though. A ten foot per minute ascent rate is simply noting that your depth has changed 10 feet when your timer clicks over a minute -- if you've gone up ten feet and it hasn't, you should stop for a little while until it does. Not too complicated a concept, and you don't need an ascent rate alarm to figure it out.