As a BJ-A owner, and since it's just about the only mech that I use, I feel like I can speak to this pretty decently.
Here's my build.
The BJ-A is a fun little guy, but that doesn't mean that it's a good mech. For the decent things that it does, it's got a lot of cons.
1) The BJ-A takes a lot of low-tonnage, one-slot items, meaning no Ferro for you. The small engine forces this; you only have 7 slots available with Ferro and 6 MG and 2 LPL. 3 of those are taken up because you need a tenth DHS. Leaving just 4 slots, not enough for 3 tons of ammo (which you will need) and a few JJs (which are the only real reason to take the BJ-A over any other BJ).
2) MGs are awful. I estimate that ~80-95% of my damage is dealt with my 14 tons of LPL, with the last 5-20% being taken care of by my 6 tons of machine guns. In a perfect world, the MGs would be dealing around 1/3rd of my damage, but they definitely aren't. I'm considering a
different build entirely that just gets rid of the MGs, and I'm pretty certain that it would do better.
3) Your JJs aren't as nice as they should be, but if you've ever played with JJs before, you already know that.
Unlike what other people are suggesting, I play my BJ-A as a brawler. The facetime is murderous for you, if you want to keep your MGs going, but if you pick targets intelligently, you can do okay.
You're not going to get huge damage out of this mech; it's as maneuverable as a heavy without the armor or weaponry, and you feel that. Getting to targets is a toss of the coin. Expect lots of inconsequential assists, though.
As others have said, the Shadowcat is going to do it better. Wait for that to come out, instead, would be my suggestion. Faster, with MASC, with more JJs... not really any reason to buy a BJ-A now.