Astero is exceptional ship for exploration. Last patch did not change a thing on that. But since you are very new as you write, then I would advise against it for now. Use cheap T1 frig instead and learn basics of the tradecraft in it. Only after that, shift to Astero.
Concerning exploration - Astero is superb for hacking relic and data sites in J-Space (only pirate faction sites in C1-3 class), very good for Nullsec hacking, and superb for low sec hacking.
It can do some basic combat sites, but you will be limited by not that great DPS (despite good application, you will be around 100). There are better ships for this, like Stratios, T3D, T3C. Don’t forget ship sizes restrictions on entering combat sites though. Astero can get even to the lowest tier.
Astero can get into limited sleeper cache, since it is frigate, but the loot is usually not mind blowing. You can go into Standard and Superior Sleeper cache. It is dance on thin ice, but you may do some part of it.
And you can fit it to survive ghost site blast in high sec, but it is specialized fit with rigs, not that much suitable for other exploration.
Mobile depot kills most of the cargo hold which Astero has and I doubt that it will be compensated by benefit of refitting. I would not use it here.
Overall Astero is superb. If flown properly, it will reward you by riches and fun.
We didn’t scratch the thing and yet it is wall of text. It is too big topic. Hit me in game or just post here any specific questions which you might have. Worst case scenario I will tell you I don’t know, but Iam sure somebody else will have the answer.