You may have seen me mention it more than once, but check out
http://bit.ly/STOShips .... make a copy for yourself like the instructions mention.
Now you have a sheet to play with. Go to SHIP DATA tab and turn on "Filtering", now, since you said you wanted a Zen or Fleet Ship, and you are very limited on EC, I recommend you Filter the "Tier" tab and turn off Tier 1-5 (leaving 5-U through 6 & Fleets). Now you said federation, are you romulan? if so, you are limited a bit, if not or whatever, choose the "Faction" turn off "ROM" & "KDF" Leaving you with FED & NON.
Now on the "COSTS" filter out any of the "LB" "ANNIV" "DAY" "CERTAIN" & "EVENT" - this leaves you LOBI, ZEN, FC+FSM.
You may not have x Lobi, but with 5000z you can buy keys, open lock boxes, and get lobi while doing it, and possibly a LB ship, but these are possibilities (you can buy 50 lockbox keys, and at ~8 or so lobi per lockbox as a possible average, its maybe 400lob; sometimes you get more or less)
Once you've done this, it gives you a wide variety of ships to look at. 137 to be exact
So you are asking us to tell you out of essentially 137 ships which is best for you. That's a tall order, but we want to help. After you do the above, take a look at some of the data there, like front weapons & rear weapons, hangar pets, console slots, notice how MOST of the tactical ships that have MANY tactical console slots have their BOFF slot for Commander as an Engineer? Stupid isn't it? This is where you can swear at Cryptic.
You'll also notice MANY of the ships have some pretty NEAT universal consoles on them. This gets into what Ed said above; because some of the builds you can do will take advantage of these consoles. DPS builds require things like massive boosts to aux energy, and use batteries, some of these ships give a boost to power of weapons, or engines, or aux.
In the meantime, since you do have low EC and some decent Dil, but you can never have enough dil, I recommend GRINDING dil like its going out of style. Why? Cause Edarta and everyone else here is going to tell you to get a Plasmonic Leech Console, this is only ONE console, but it costs like 45mil on the exchange. You will want to get more upgrade materials to upgrade the rep-gear you'll grind. So don't be shy on collecting Dil
To Ed's point, Escort players spend a lot of time "zipping around" so there is a lot of movement involved, and they use weapons that have very narrow firing arcs, so they are like a 45 calibur hand gun in the hands of a motorbike rider, they have to point and shoot, but the bike needs to be moving at full speed while doing this, so they spend a lot of time flying through the thick of it or zipping back and forth, or circling like a mosquito.
Carrier players, play in a rather slow motion and fly slow as they work in battle, generally staying at a fairly far range, and are rather tankie. I've seen many built with kinetic or cannons.
Cruisers are the style that take a beating and keep on ticking. They use beams usually. They fly sideways to take advantage of front and rear attacks.
Science ships, (and this is true for some escorts and even some cruisers), are built to do the special tricks like tykens rift, gravity well, radiation damage, etc. These builds are specialty, and usually are a DPS support build. They still need cannoneers or beamers in the party. Science builds can do MASSIVE DESTRUCTIVE DAMAGE, but thats usually in the form of debuffs, and other unique damage to the enemy.
OH, btw.... are you looking to PVE,.... or are you looking for DPS in a PVP?