I love delay -- digital, analog, and tape. Each has its uses, all are wonderful used in the right way, and there are some fantastic options out there. So I'll share a few thoughts about choosing one.
If you're going in front of the amp, as I do, and you have the amp set for some grind, you might find that you like the delay repeats mixed fairly subtly, and you don't necessarily want a lot of repeats, because as they decay and each one gets softer, the amp distortion becomes a greater factor. In fact, with guitar, repeat times such as how many milliseconds of delay you can coax out of one of these things isn't really all that important a spec -- in most cases, every pedal on the market has sufficient delay time these days to work for most players.
But every type of pedal or box will sound different. Digital pedals have tremendous flexibility, and while their emulations of the analog bucket brigade and tape effects are pretty good, they're also not as realistic as their manufacturers make them out to be. I like digital pedals for the things that they do that no analog pedal or tape echo can do, and there are plenty of things that exist in that way, such as echoes that duck out of the way when you play the next note, tap tempo, syncable tempo, and the list goes literally on and on.
Analog bucket brigade delays have a certain thing happening that even the very good emulations by Strymon, TC and Eventide can only approximate. There's a roundness to the sound that does alter it, but in an interesting way.
Finally, nothing sounds like a real tape echo. Having worked with them in the studio for years, it's easy to see why - the ones based on the old Echoplexes and the old machines themselves, are just ancient, weird technology! The machines aren't exactly high fidelity devices, the cartridges are these wobbly, flexing kind of things that have to be held in place with thumbscrews, the preamps distort, and so on, but the end result is a glorious richness and saturation that, I'm sorry, has managed to elude even the best digital designers. When I play a digital pedal emulation of tape in the studio, and then switch to a real Echoplex, the difference is startling. There's a glue holding that sound together and you cannot get it digitally, at least not yet.
On the other hand, analog tape isn't for everyone. The machine itself is kind of noisy, the machine's heads need to be cleaned every few weeks, the tape needs to be replaced. It's not going to be velcored to your pedalboard. So there's some minor work around that. It's not a chip, it's a machine, with all that implies. I love it, I think it's irreplaceable in the studio world, but most people would feel that they don't need it. Just don't take mine away!
Anyway, because digital pedals are so very versatile, and can at least give you an introduction to the various types of delays that have been designed plus new ones, that's the way I'd go to start out.