T3 Destroyers are best choice because you can use them for 3/10 DED, anomalies up to 5/10 and Clone Soldier hunting. They align fast and warp fast. The best of them is Jackdaw, but Confessor has also merit as you don’t need to buy ammo too frequently. They have decent cargo.
Disadvantage is that they need tons of skills to make them efficient and they require some practice of flying and doing the sites, 4/10 are not as easy as just warp in, stay in place shoot everything, it requires some strategy and tricks to do it like shooting only the structure or ship with loot then warping away and waiting up. You better start with something else first.
So, if not T3 destroyer the other option is Sunesis (4x t2 drones and 3x turret/missile can imitate t3 destroyer in about 50% efficiency, for 3/10 is it still really good for 4/10 not so much and depends on faction but doable). Still requires quite a practice and a little of bling too (I use deadspace shield booster worth of 40mil but maybe if I was using omega clone with higher skills I would not need it).
Another option are t1 or t2 (if you have the skills for them) cruisers. Railgun Vexor is the ship I used in beginning and it was capable of doing DED 4 easily, but usually t1 cruisers will struggle outside of their “region”. Caracal will be probably exception because of the damage profile advantage of missiles and no reliance to drones which are in Blood Raider 4/10 quite useless for example.
If you find t1 cruisers too slow and inefficient and you don’t have skills to fly t2 cruisers then Gila is best ship. It is both drone and missile ship so you can use it both afk-style for easier sites or anomalies and active style for tougher sites. It can also do anomalies up to 8/10 and I was able to do drone DED 5/10 with it as well, but drone DEDs are crap and unfun to fly. Other pirate cruisers will work too but Gila has the best DPS and is most universal and easiest to use. In most situation you just sit still and shoot and controll drone aggro, or slowly approaching accelleration gate or some npc. Other pirate cruisers usually need much more than that.
Stratios really isn’t good though. It has no bonuses to weapons so it is slow. The bonuses to scanning are worthless, unless you hunt Sleeper sites. Otherwise you can scan anything with unbonused ship with basic t1 probe launcher and basic probes without noticeable difference in speed or difficulty of the scanning. Okay maybe not few relic/data sites but those are not the sites you want to do with Stratios anyway and in highsec especially.
Astero is terrible ship for DED sites. DED 1/2 are not worth it and they probably only appear in 0.9 and 1.0 as I never found them in 0.6 - 0.8 (but curiously enough I found them in lowsec and nullsec) there is no point to visit systems like that. DED 3 is doable but slow and the main disadvantage is cargo. Frigates have very limited cargo space, basically you can only pick up the deadspace module because if you pick the Overseer Personal Effect items you will be full after one DED 3/10.
Sure cloak means you can do it in lowsec but then you also need to train cloaking for a month. If you already have cloaking then Stratios will do much better job and as I said, stratios is actually bad for DED sites. Additionally, T3 destroyers, Sunesis and Cynnabal can get sub 2sec align (with a small refit) and thus fly around in lowsec easily as well and they will be faster than Astero in doing DEDs.
But of course if you are flying astero looking for sites and you find out DED 3 or 4/10 and you are too far from your base to reship why not? But if it is an escalation I would rather use Worm than Astero, he is almost twice as quick and cheaper. I don’t ever bother to refit for travelling, but I am flying in lowsec with low activity so gatecamps aren’t a thing and one guy sitting on gate never caught me and even if he did I would be able to return to gate.