So, you had to choose one of the most pain in the rear items to cut!
In all cases, this is not an in the home, basement or attached garage type of project!
The best method of cutting acrylic sheet is with a 'hot' (red hot) cutting wire. Most all DIY'ers do not have such a tool, since it can be expensive and rarely used. So now, it depends on what you have in the way of tools?
First item: Painter's Tape! Get it wide and do not use it sparingly! Leave any paper coating, which commonly is in place when you purchase the sheet in place. DO NOT REMOVE IT UNTIL YOU ARE FINISHED
INSTALLING THE ACRYLIC SHEET. Any place there is no paper covering, cover those areas with painter's tape!
Second item: The Cutting Tool; Please, Only Use a New Blade! Also, buy a back-up blade, running back to get another is a pain! This is not the place to cut corners. Sorry, I couldn't help myself.
Let's base this with a common hand held Jigsaw. And lets, let this term cover anything that moves the 'fine tooth' cutting blade up and down. Purchase the maximum number of teeth per inch, blade you can find at the Big Box/Hardware store.
Always, let the blade do the cutting, never push it! NOTE: Cover that part of the Jigsaw face that will be riding on the Acrylic Sheet with two layers of painter's tape. A smooth cover is important - hence the reason for getting the tape wide, so that a single piece covers. Most guys will grab for their Cut-Off-Saw, but it will be difficult to control and more than likely crack the acrylic sheet if not very careful. There are other tools, and if you have them, you know their advantages, proceed with them (far upper-end: a cabinet series, table saw with special high tooth count, thin saw blade).
Third item: Sandpaper 150, 300 and 600 grit and a sanding block. A Buffer - if you have a drill, you only need to add a buffing wheel to it (think buffing out a car's hood, but does not have to be that wide). NOTE: Never use a buffing wheel that has been used to buff acrylic on you car!
Fourth items: Pencil and straight edge! Note: Slight curves can be a pain to create, so target something that you can use to create the curve you need: like at five gallon bucket, its cover or like item that has a curve near what you want, larger pots, round planters, etc...
Layout your design and if you are making several pieces, try setting pieces side-by-side to reduce the number of cuttings. Remember that you will loose the blade thickness with each cut, so add that thickness to your measurements!
Do not push/rush the cutting - the faster you push the greater the likelihood of causing a crack! Once you have all the pieces cut, use the sandpaper starting with course and moving to fine (with a sanding block) to flatten and smooth the edges. The drill with the buffer is now used to buff the edges to a clear finish. This can also be done with a heat source, but that does require some expertise, get it wrong and you burn your acrylic sheet.
During Cutting, Sanding and Buffing, work at keeping the acrylic sheet still. If you have clamps use them, but use them properly with something like wood strips to keep from marring the acrylic sheet. Do not let the acrylic sheet hop or bound around - it will crack it!
NOTE: Buffing creates heat and that is what causes the acrylic edges to 'melt' smooth (clear). Use a scrap piece to practice with! High-speed, light contact! NOTE: IF the edge can be seen, it is worth this extra step to get is clear and therefore get a professional like finish!
Remember - Slow Down!
P.S. Drilling Holes, always use a wood board under the acrylic sheet and like cutting, slow down using light pressure to cut the hole. Old, used drill bits will cause heat. So, you may want to buy new set. FYI: Buying a single drill bit is costly. Look for a set you can use for other projects that is in your price range. Any drill bit set, which stated for use with metal will work fine.