In order to get a right angle cut you have to cut it on a table (circular) saw. If you cut it by hand or on a band saw then you have to straighten it with a router (or a milling machine if you have an access to one).
For smoothening the edge (or surface) you'll be using sand paper. For this make yourself some sanding blocks in various grits by sticking the sand paper onto a timber (or any other) block using a double sided tape.
Start with 100 grit to take the roughness. Then sand it down with 180 grit and then something like 120 and 240 grit. If you are going to bond the edges then you do not have to go any further as the glue will fill in and the whole thing will come up transparent.
Apart from anything there is a deliberate need for not polishing the edges which are going to be glued. If the surface is polished to total clear then if you do not bake it in the oven, as soon as you apply the glue the surface will crack hairline due to stress.
For gluing there are three main adhesives.
First one is Tensol which comes in two parts. There is also single part type but I never used it. You mask off the the areas that you do not want the excess glue to go onto. Apply the Tensol to the area and position the part to be bonded. Now the excess Tensol will spread over the masking tape. Do not touch it. Leave it to dry for an hour or so until the Tensol chewy hard. Then carefully cut the excess along the edges using a surgical scalpel (I use Swann-Morton 10A, 25 and 26 blades). Remove the masking tape carefully and leave the whole thing to set for 24 hours. This is a permanent bonding.
The other two types of adhesives are Chloroform and Dichloromethane. I don't use Chloroform as I suffer from migrane terribly. Dichlo is lesss smelly. Both of these are in water consistency. All you need is an artsist's paint brush of an appropriate size. You hold the pieces together, dip the brush in dichlo and touch the edge. The dichlo will run straight in. Then repeat it all the way. In a minute or two it will be strong enough to hold itself. After half an hour all will be rock solid. But this is not as permanent as the above method, though as long as you don't force it itwill stay for years. I stil have things that I glued twenty years ago.
For polishing the surface to totally transparent, after 240 grits you continue with 400 and 800 grits. then use 1000 and 1200 grits but this time you have to dip the sand paper into water and then apply it onto the acrylic gently. Once you are happy with the surface then take a bit of balsa wood or even thick cardboard, apply some T Cut (for polishing your car's paintwork) and rub the surface down to water clear.
There is also flame polishing but it is not really a hobby application.
Also some people may advice using polishing mop on a drill. I do not reccommend that for polishing edges as it will take off the corners. For surfaces you also have to be careful. If you go too hard or stay on for too long you may wear out the surface and create a "crater". Getting rid of it means starting the sanding down procedure right from the beginning. Even then there is a risk that it never gets right. If the piece to be polished is managably small then the best way is to have the balsa wood or the cardbaord taped up on a flat table surface, TCut applied and the piece rubbed on a circular motion.