So far people suggest the One Silver Bullet ship for running L4 missions, but all those ships are specifically for full-clearing them and spoiler alert they will NOT be able to run Anomic Missions at all - anything bigger than a cruiser or T1 battlecruiser won’t even be able to enter any the sites.
Anomic Missions can be offered by any L4 security agent and are very good money-makers, awarding more LP/isk in the rewards and even the possibility of faction loot from the rat(s) you kill. You can chicken out and just decline or quit any Anomic Mission without any penalty (so you can just go back to full-clearing your safe cozy Angel Extravaganza missions), but when you equip yourself properly to run them they’re very quick clears and very predictable sites with little risk.
But the rats in these sites are VERY DIFFICULT encounters, requiring you to bring hard counters to the table. They will tackle you too so if you don’t bring the right stuff it will be gameover! (please just test whatever you are planning to use on SISI first, losses on SISI are free).
As such there’s no single Silver Bullet ship that can run every Anomic site but there are two ships that can run most of them: the Garmur (rockets) for fast-clearing Anomic Teams and Nergal for fast-clearing Anomic Agents. The Garmur can even keep the exact same fittings for all four different Anomic Team sites, but the Nergal does need its own specific set of fittings for each of the Agent sites however.
Use a Praxis to blitz any speed-clearable regular L4 you get in-between Anomic Missions, decline all the ones that force you to full-clear the site if you have the standings to take the hit (angel extravaganza, worlds collide…), having Connections trained to at least IV and Social to V helps with that. Later on you can think about getting into a Machariel or a Marauder (Vargur notably) but not before min-maxing your skills for the Garmur (all missile supports and navigation skills that improve velocity and agility) and Nergal (gunnery supports, armor tanking, and capacitor). You will need a fraction of the SP to get a Garmur and Nergal and be able to clear the majority of the Anomic Missions as a result vs. just beelining for a well-skilled faction BS or Marauder…
There are many guides on how to run these missions and how this speed-clearing playstyle (aka Blitzing) works. One example here: Burner Mission - Ship advice to solo them including fittings
Or you can just slowly full-clear everything and also add Anomic Missions to your diet by training those ships too. You’re in highsec so it’s not like you’re gonna get probed and tackled if you spend more than a couple minutes in a mission site…