Hi ! We currently have a 6 week old who wriggles and wriggles in her sleep to the point where she makes it all the way to the side, or up the basinet. Currently, she sleeps in a love to dream suit and I place her at the bottom of her basinet in our room with a blanket tucked tight but she manages to wriggle to the sides. The basinet does have like a netting around the sides, but the part where she can put her face when she does manage to get to the side is like a cardboard with material stretched over it. My question is should I place her in a sleep suit with arms free or should I use a swaddle with arms free and no sleep suit? And should I leave in the basinet in our room as she is only 6 weeks and I can check on her regularly though the night or move her to her cot which unfortunately will not fit in our room?

There is no need to stop your baby from wriggling & changing her position, but it is important to make her environment safe in light of what she is doing.
Many babies will wriggle & change position (like you describe) at a young age.

Often this can mean that baby is soon going to be rolling.
You could try unswaddling now or swaddling (or swaddle suit) with arms out.
Often these babies like their arms free or like to touch their face or suck fingers & will wriggle to get free.
How does she go with tummy time when awake?
When she starts to roll, she will need to be moved to her cot.
It is good to have her in your room for as long as is possible, but if she is rolling it is important, she is in her cot.
Safe environment takes priority over room sharing.
Parents are not expected to observe their baby constantly. If your baby is sleeping in a separate room check baby regularly to ensure that the baby remains on the back and the head and face remain uncovered (as baby grows beyond 5-6 months they will move around the cot and roll over; settle baby to sleep on their back but let them find the sleep position they feel most comfortable in. A safe cot and safe sleep environment is still necessary for babies older than 5-6 months).

https://rednose.org.au/article/room-sharing-with-baby

Most babies will be rolling over by 4-5 months…....some earlier, some later.
This is very normal as babies grow & become stronger many babies then prefer to sleep on their tummy.
*It is important that you move her from bassinet to her cot & cease wrapping once she is rolling or attempting to roll.
*Baby needs arms free & the space of the cot to roll safely.

Once she is rolling it is important to make the environment as safe as possible for this to occur.
Continue to always place baby on the back to sleep.
Ensure cot mattress is firm, well-fitting & flat.
Ensure there is nothing loose or soft in the cot.
Preferable to use a sleeping bag when rolling that has appropriate size neck & arm holes.

Red Nose has the following information when baby is rolling.
Give baby extra tummy time to play when awake and supervised as this helps baby to develop stronger neck and upper body muscles which in turn enables them to roll back over.
Make sure that baby is on a firm and well-fitting mattress that is flat (not tilted or elevated).
Make sure that baby’s face and head remains uncovered (do not use lambswool, doonas, pillows, cot bumpers or soft toys)

As babies grow and develop they become very active and learn to roll around the cot.
At this time, continue to put them on the back at the start of sleep time, but let them find their own position of comfort.
By this stage it is not necessary to wake during the night to turn baby over to the back position

Do not use any devices designed to keep baby in a particular sleep position.
https://rednose.com.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over