Echoing that baby wearing CAN be very expensive -- I wore my "baby" for YEARS with exactly ONE sling that I got second hand. The thing is in tatters. Many years later I had my second and the selection of slings is amazing now! Global import economy and industrious babywearers, made for quite a change.
My advice is that YES you can absolutely start babywearing at 3 months. I agree with a PP who said that a pair of arms are probably the best for the first couple of months anyway.
As far as what type... well, I don't even know what a Boomba Baby wrap is. Oh, I looked it up and it is a knit type wrap. Gosh, check Craigslist (if you're in the states), consignment, or those big swaps. Because those knit carriers are relatively affordable, user friendly, and can only be used for a short period, they are ALWAYS being sold second hand. Of, better -- post on Facebook (or have a friend do it for you) and just ask around if anyone has one in storage. There's nothing that eases parent guilt over all the stuff we got for our baby that we didn't use it's lending some of it out to new parents!
As for other options -- a woven wrap is more versatile because you can wear your child in one for WAY longer. But, they are very expensive. They do have a very good re-sale rate though so it's not a bad "investment", however that also means it's difficult to find a good deal second hand. You can also make a wrap out of gauze, which is more affordable than most woven fabric.
I am a big fan of the open tailed ring sling in a nice woven fabric. My favorite is the Maya Wrap (specifically the older, more traditional fabrics). That was what I used for my first back in '01 when that, Didymos, New Native and OTSBH were the only game in town. With my second I rented a Girasol woven wrap, made a gauze wrap, owned an Ergo, and tried a whole bunch of other slings and still preferred the Maya, which I bought on Ebay for like $20. If you go the used Maya route, they have updated their shoulder design and it is much better but there are online tutorials for how to do it yourself. If you have a sewing machine it's like a 30 minute project.
The only truly inferior sling that I've tried was a modern machine woven fabric ring sling. These fabrics (like the ones you get from a typical fabric store) need to be doubled to make a sling and they are very inferior in terms of how they slide in the rings. So, yea, fabric really does matter. Watch out for that.
Otherwise it's just a matter of finding was try a few things. See if your city has a babywearing group. And, good luck!