Hey welcome to the forum--- it sounds like you have a head start on a lot of folks that take up fly fishing without having any experience fishing with other gear.--- so you know where they live, and where to look for them.
Early in the season when water is high in streams--- and in large bodies of water like Ashoken, you might try some big meaty streamers and perhaps a sink tip fly line, especially if you're fishing in the reservoir--- it just might get slammed by something.
Local fly shops are great sources of info, and you can jump start your fly fishing career a good bit by hooking up with a local chapter of a group like Trout Unlimited--- most chapters have informative monthly meetings, formal or informal trips to local waters, casting and tying clinics, and it's a great way to meet up with some new fishing buddies. You can do a search to find a local chapter near you here Council-Chapter Search | Trout Unlimited - Conserving coldwater fisheries
And the NY DEC website has a lot of info on special water that is open all year, general regs, DEC Access sites on different streams.
And there's a lot of good info on a local guide's site named Jerry Hayden for you to check out, including links to a Delaware River hatch chart and some basic info on some of the bugs.
Wild Trout, Delaware River Fly Fishing Guide Jerry Hadden
The info for the Delaware on Jerry's site will also apply to the Esopus. Most dry fly activity doesn't really start until mid April, and streams will probably be roaring for awhile with all the water we've had. And the first at least semi-reliable hatches start in April for the most part anyway:
Blue Wing Olives size 18-20, this is a big deal hatch that lasts a long time, and also many different species can be matched by Blue Wing Olives. A must have in your box all season.
Blue Quill size 18 often hit or miss, often lasts only a week or two in most locations, usually starts when water temps hit 50 degrees
Quill Gordon size 12 and 14 often hit or miss and often only lasts a week or two in most locations.
Hendrickson (females) and Red Quills (males) size 14-16 a big deal hatch, long lasting over several weeks most years from mid April well into May, and very prolific on many Catskill streams
Using the general hatch chart for the Delaware and some help from a local shop (or your new TU buddies) you can zero in on the other important hatches on the Esopus (like the Isonychia and many stoneflies). With a little research you can also learn where to look for them in the stream (fast water or slow, gravel or mud bottom etc) time of day the hatches tend to occur, and the most productive patterns and ways to fish different stages of the hatch. (there are a number of online resources for this, as well as a ton of books depending on how nuts you want to get with this, but advice from local experts is often your best bet.)
And the folks here are a friendly bunch so keep asking questions here, I'm sure you'll get a ton of advice, and there's a lot of info in old threads and in the FAQ section.