Somewhere fun/safe to put baby when you are busy- either a swing (they make the fold up smaller kinds), bouncer, or rock n play. You can get something that folds up when you aren't using it to save on space!
(Portable swing: https://www.amazon.com/dp/B00E3RKC36/ref=cm_sw_r_awd_yC.Mvb4YWFQ52)
There are awesome, swings, chiars, bouncers, bassinets that rock all great options. I had a swing and a bouncer and a bassinet. But the way I actually got him to sleep as a baby was by making him stay awake as much as possible during the day. My son was sleeptrained thought the night at 3 months by this.
Ingenuity Cozy Kingdom Portable Swing https://www.amazon.com/dp/B00E3RKC36/ref=cm_sw_r_cp_apa_i_JX4cDb723QKDX This is the swing we used we actually got it secondhand for free after the first one we bought by Graco broke.
Graco Pack 'n Play Reversible Napper and Changer Playard, Basin https://www.amazon.com/dp/B01BGVLJ4W/ref=cm_sw_r_cp_apa_i_RZ4cDbGWK70YK this is the pack-n-play he slept in in our bedroom in the infant sleeper which slips over into a changing table he slept in this for 3 months until he was too big and we moved him down at 6 months he with into his own nursery.
Bright Starts Playful Pinwheels Bouncer https://www.amazon.com/dp/B00KHR7TPK/ref=cm_sw_r_cp_apa_i_q14cDbA96K9Q5 this by far was his favorite this was his bouncer and he loved this thing until he was just about to big for the buckles in it from the time he was a newborn infant until about three months.
(This was the best at rocking him to sleep and it was at the perfect angle we could actually give him a bottle in it without him choking once I stop breastfeeding)
Fisher-Price Jumperoo: Animal Activity, Blue https://www.amazon.com/dp/B071ZSFWCG/ref=cm_sw_r_cp_apa_i_W04cDbX59XB3Y after he was three months old and too large for his bouncer we got him this jumper again secondhand you paid about $25 for it
I really hope this helps!
I have 2 big boys (11lbs5oz and 10lbs4oz respectively), ages 3 and almost 4 months.
They both slept in a bassinet for about 3 months and transitioned to a pack n play on the bassinet setting. When my oldest started to roll, I moved the bassinet mattress down to the base.
Bouncers and low swings are a better option than anything tall. They have a larger range when it comes to weight and size limits, and when you look over and see a leg hanging out...it's not quite as scary. I have this and a bouncer I got for $5 at a garage sale.
Someone suggested the Mei Tai carrier to me for big babies. It's been a lot more comfortable than the carriers with clasps.
The carseat we have is a Graco click connect with a compatible stroller. Whenever possible, we bring the stroller and lock the carseat into it. My oldest outgrew the bucket seat at around 9 months and has been in a convertible seat since. There are a lot of good convertible seats that grow with even a big kid. I have the Graco MySize65 - I'd get the 4Ever if it wasn't too big for my Honda Fit.
If all else fails, a comfortable floor mat in a safe place works great. I bought a big shaggy fleece rug. My baby loves it because he can see me and everything going on. When he gets more mobile, I can put a baby gate around it.