Cutting straight is a problem with a scrollsaw and not a lot better with the small bandsaw either. A wide blade on a bandsaw with a very rigid frame is better but expensive.
You can cut fairly straight with practice and a deeply scored line will help.
There is a website which suggests holding a steel rule along the line and letting the blade contact the rule. Not tried this but it may work or may damage the rule.
It is a matter of choosing the right tool for the job. A £3 handsaw from B & Q will cut straight on DIY size jobs if you practice. A hand Mitre saw ( picture frame saw ) is very handy for small precision jobs up to 6 inch and is an essential item for me. Get a large one though.
For cuttting medium size jobs a tenon saw works OK but better is a pull saw either Japanese handle type or european handle type. These very fine blades cut on the opposite stroke to European saws and it helps to keep to a straight line. Clamp the work firmly or use a bench hook and practice slow steady cuts. Axminster list several pullsaws with european handle for about £8- I suggest the finest teeth are best for aeromodelling.
Worn out saws are the very devil to cut straight lines, even the cheap £3 saw will cut better than a great make that is worn.

If you want to cut stripwood you need a saw bench, but good ones are expensive .
Balsa stripwood is cut with a balsa stripper like the SLEC one. About £8 I think.
You can make the straightest possible cuts on ply up to 3mm and balsa up to about 6mm by using a Stanley knife and a straightedge. Use a brand new blade and use repeated cuts along the same groove. Clamp the straightedge if possible. If necessary turn the wood over and run the knife along the reverse to finally release the part. This technique is great on liteply.
To sum up see which of the above saws fits you current project and have Father Christmas buy you that instead of socks or aftershave. Spend Boxing Day practising until your muscles know how to cut straight. The secret is sharp saw, clamped work, steady strokes and practice!