Mine is almost 19 months old. I'm a first-time mom as well and it was alot to handle. I had no help (no grandparents, babysitters) except for my husband who also works from home. He can hold her sometimes while he programs or watch her while he's taking a break. Some things I use to entertain her. She likes being on the countertop and plays with bottles. They really entertain her so I can do my kitchen stuff while keeping an eye on her. She watches educational videos on my phone and is pretty engaged. She plays with the walker, "busy board", anything that rattles or clinks, etc. A busyboard is something you can make yourself as well. You just take some plyboard and put random stuff on it like a switch, doorbell, gears, buttons, etc.
I used to do the carrier thing but my baby is way too heavy and i don't actually get much done. We have a playpen but she cries because she's by herself. It works better if someone is around her, so a playpen nearby while you're working. You might also want multiple playpens. And the stroller thing is good. When I was outside working in the garden, I would put her in the wagon or stroller. My daughter is starting to walk so it'll be easier when spring comes and she could maybe help me outdoors or in the kitchen. Also, there's a toddler step stool that you can get when she's older.
As for crying it out, I tried when she was younger but it was hard on me and my husband didn't like it. I only had to use it a few times when I had no choice. She's in her own room now (she sleeps in her playpen on a twin mattress) so I get wayyy more sleep. She'll cry in the middle of night but she'll go back to sleep. Before, I would go to her room and nurse her to sleep again, and then sneak away quietly. For naps, I still nurse her to sleep, and it's pretty smooth. I also nurse her whenever she wants comfort.

