Speaking as a complete novice here... how do you know what model a vintage Singer is?
If you have narrowed it down to Singer; black and beige domestic models, it should be manageable for a beginner ;- )
Look at the bobbin plate; if there are two covers crossing the entire bed of the machine it's a vertical shuttle machine. It's usually either a 28/27 or a 127/
128. The older pre 1900 models in this group are Singer 12 and VS1 and VS2, which developed into the 27 and 28, and ended up as 127 and 128. We sort of pair up model 27 and 28 because they are identical except the 28 is 3/4 size of the 27. It's equivalent with 127 and 128. These are also called long bobbin machines, and are easily identified by the bobbin winder too.
If the bobbin cover is at the left short side of the machine, it's a round bobbin machine. Singer's first was model 15, and there are lots of version of this. It has a bobbin case you take out very much like Berninas CB hook and bobbin case. There are lots of sub version of this model, with and with out stitch length lever and reverse stitching.
In 1900 Singer introduced their first drop-in (horizontal) bobbin case (some call it basket, and insist it's not a case),
model 66. This model is still one of the nice and easy to use; needles and accessories are standard and in plenty. There is a 3/4 size version of it; model 99. In 1928 (I think, some sources date it to around 1930)
model 201 was introduced; it has a rotary hook and race, with the same bobbins as the 66. This is a straight stitcher and was in production until the early 1960s, and if you can recoginse the stitch length lever and the top tensioner it's easy to identify.
In the early to mid 1950 Singer introduced the beige color, and two tone beige-brown. Model 201 now came in a beige aluminium cast version given the number 201K23. Model 99 suddenly came in a beige version, and new look; it was given a new model number 185. By the 50s swing arm zigzaggers became more common, 306 is one of the early ones, 319/320 the later 401, 411G is held in high regard by many. With the zigzagers freearm version turn up.
I might have flooded you with simplified info, but in general, take a look at the bobbin case, shape of bobbin plate and position of the top tension mechanism. All the old models went through slight changes and updates as the decades went by, but in general kept their main build and internal parts. The black japanned machines came in all sort of decals and decors, so keep an eye on other details to identify.. Over all body shape is of course a good indicator too.