The truefit works well for newborns, but the RF weight limit is just 35#. However a very tall/skinny or long-torsoed child might last longer rearfacing in the TF compared to something like the MyRide because it has a taller shell. So if a child outgrows the MyRide by height (or another 40# RF seat) before 35#, then the TF will last that child longer. However, unless you have a reason to suspect that your child will be exceptionally tall & skinny or long-torsoed, the TF probably won't last as long for rearfacing.
(Incidentally, a seat is outgrown rearfacing by height when there is less than 1" of hard shell above the child's head, measured as in
this thread.)
So, for seats <$200 with a 40# RF weight limit that will work for an infant, your choices are a Graco MyRide, Radian 80SL (on sale), and Britax roundabout 55 (or maybe a marathon70 on a good sale) with infant insert. Installation-wise, the RA55 is *generally* going to be the easiest, then the MyRide, then the Radian. But the ease of installation really depends a lot on the car, so if you can try the seats before you buy, then you'll know for sure if it works well for you.
If you don't have a lot of front-back space to work with, the Radian might not fit very well.
ETA: Other options might be the Evenflo Triumph 65 and the Evenflo Momentum 65. I'm not 100% sure on how well they work for newborns, but I think they generally fit into the "not amazingly good, but usually okay" category. I'm sure someone will correct me on that if I'm wrong.