what kind of paper cuter did you get? one of the old guillotine type like schools used to have? or one with a razor blade that slides back and forth down a track? if it's the second type you just have to apply a little more downward pressure on the bar that holds it down. i kind of walk my hand down the rail just behind the sliding razor. if the guillotine type good luck. i have never been able to get them to cut plastic right. i usually use a good sharp razor and a metal straight edge to cut my plastic, most plastic you just have to score the surface and then you can bend and snap it the rest of the way through.
as for curves, there are several methods.what you use depends on the situation, or your skill/preference. it will also depends on how tight of a turn you want to make. a real tight turn and heat would have to be applied, i use a variable setting heat gun for this. it will take some planing around to get used to applying just enough heat to make the plastic malleable but not melt it. the trick is to keep the heat source moving over your entire piece not just one area.
nice sweeping curves can be achieved by creating a skeleton underneath in the shape of the form of the shape you want. like this:
then you can bend the plastic over it and glue it down.
here's a link to my photobucket on that model. i had to pretty much scratch everything on it. and almost the hole ship was a complex curve. there were some times i had to heat the plastic sheet and use a skeleton to get the achieved angles.
http://s1015.photobucket.com/user/raser13/library/probert richter ambassador class?sort=3&page=1
you can also see where i used a picture of the ship to aid in cutting and layering the pieces to make much more complex pieces. plus if you go through the other models there you will see alot more of how i scratch other things and used found stuffs. i have boxes of awesome shapes.
i to recommend making a smaller model first. one to try out ideas, or practice needed methods.then build up to doing the model that you really want to do. you don't want to have an idea in your head that is that one model you want to turn out perfect, try and do it, and have it not turn out to good because you rushed to fast to get there. it will frustrate you and might turn you off from trying again. i am not saying don't try to do it!! or to just give up now. not by any means! quite the opposite. i just don't want you to bite off more than you can chew and scare yourself into not trying again,
as for thicknesses of plastic to use and buy. i don't think i've bought styrene in years. for skeletons and internal structure i use old credit cards and fake ones they send in the mail. my family and friends save them up for me. i've also have a few stores that save me old plastic signage. you have to usually talk to managers on that one. but i also nab plastic garage sale signs that people leave up. i give them a week after the sale date. then the sign is mine. plus it beautifies the area. i also save flat pieces of clear packaging. all of these can come in different thicknesses. i just find one that's the thickness i need and start cutting. if it's not thick enough i stack them up.
putty and sculpting putty will also be your friends. can i also recommend a few other tools if you don't have them. a compass with a point end and a razor end. a dremmel with mill bits. razor saw. pin vice with assorted bits . and a scribing tool. these are my scratching go to tools.just remember with the dremmel to use eye protection. i've seen alot of people use one with out it. that's just asking to loose an eye.especially when cutting away plastic shards, and having to get close to see what you are doing. i've embedded a cutting disk into my safety glasses with a dremmel before. if it weren't for those glasses i'd be seeing the world alot differently right now.
the only other advice i can give you is plan it out. look at where you need to start, figure out what comes next. and so on. look for things that you want to do on that next step and see if there is some thing you need to do in step one to make that happen, so that way your not having to fight something once it's all together. or having to rip something half apart to fix it latter. you don't want the story behind that tid bit. ask your self are you going to light it? if so where do the wires need to run? power supply? what is it? where does it need to go? acces to it for recharge or replacement? are you adding an interior space that will be seen, like a cockpit or shuttle bay. are there going to be people in them? what size? hallway or doors to other rooms? are they closed? or do you need to add something to be seen back there? that should get you going, and give you and idea on questions to ash yourself.
hope all this helps. pics of what your asking about are always good. lots of description if you don't have pics. and there are no dumb questions. we've all been there before. so we like to help out others.good luck.