There is some first-rate advice in this thread. As others have commented, don't underestimate the amount of time required for this. I researched and wrote the book on the Minehead Branch (pub by Lightmoor in 2006 with 2nd edn in 2011) and spent more than 20 years researching. I think there are a couple of things to be borne in mind:
1. if you are *just* researching for a model then it can be done quite quickly. To be honest, if you make a couple of mistakes its not that important and could be put right if required. Large scale OS maps and a visit to the local records office, the line society or local museum would give you almost everything you need to get started.
2. HOWEVER if you are intending to publish your research then you must be more careful. Once a work is published it will be regarded as fact and if not careful you can seriously mislead future researchers who will look at what you have done. In these cases you own it to others to get it right. With the Minehead Branch book I spent quite a lot of time debunking facts in previous books that turned out to be fanciful.
Notwithstanding that it is an absolutely facinating task. Just to be touching the very same documents that were written and signed by those who were instrumental in building our railway heritage is a humbling experience. My best moment was coming across a piece of paper hand-signed by Brunel in his capacity as engineer to the West Somerset Railway in 1857. This was in the House of Lords records Office (a source i dont think is mentioned above) where you can consult all the parliamentary evidence submitted when a railway was planned. Not normally massively useful for modelers but great for historians.