I recently bought a Trek Atwood WSD for my wife. She's about 5'3" so the size I ordered is 15".
I don't know much about bicycles and was wondering if this model is a good bike for a beginner. Also, is Trek a reputable bicycle company?
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Trek is a large reputable bicycle company. They make a lot of bikes. They're basically all good, if used for what they're made for. There may be a few models now and then that have problems, but that's true of all the bicycle companies.
The Trek Atwood WSD appears to basically be a steel version of the Trek 7.1 FX Stagger with some details to make it look a bit more "classic". It's a "hybrid", which are good all-around bikes for riding on paved surfaces. They sell a lot of bicycles with that basic frame shape. It's a very popular general style of bike, from Trek and from other bicycle companies.
Hybrids like the Trek Atwood and Trek FX are generally what I would suggest most people shopping for a bike look at first.
Definitely a good choice for a beginner, as long as she likes the bike and is comfortable on it.
If she's not comfortable on it, you should probably explore getting the fit of the bike adjusted instead of switching to a different bike. It's common to change to a different saddle and to get the handlebars moved around a bit.