Without knowing exactly when in the 19th century, it’s really hard to say what the appropriate equipment would be. Consider you’re talking about the century that saw the Napoleonic Wars, the American Civil War, the rise of the telegraph, and railroads. Standard infantry kit went from a musket to a bolt action rifle, even the actual powder used changed from traditional gunpowder to much more powerful mixtures that reduced fouling and allowed for substantially more complex firearm designs.
When it comes to overall military technological development, the 19th century saw one of the largest jumps in human history. In 1801 a cavalry saber was still a practical combat tool, but by 1900 it had been superseded by accurate, multi-shot rifles, semi-automatic handguns, even the modern pump-action shotgun, and heavy automatic weapons such as the Maxim Machine Gun.
In case the name is unfamiliar, the Maxim was one of the first, recoil operated, heavy machine guns. It was belt fed, water cooled, and entered service in 1886. You couldn’t carry these things around (they weighed something around 60lbs), but you could set them up in an emplacement and hose down anything that looked at you funny.
It’s worth pointing out that Europe wouldn’t realize how far the 19th century had really taken warfare until 1914, but most of the technical groundwork was already in place, and being used, before the century ended.
If you’re looking at 1801 to 1815, the first two examples that come to mind are Patrick O’Brian’s Audry/Maturin series and Bernard Cornwell’s Sharpe novels. O’Brian focused on naval combat, while Cornwell focuses on infantry combat (technically the first chronological novel is set in 1799.) Both have also been adapted, Master & Commander on the Far Side of the World, and multiple Sharpe novels. You’ll probably want to supplement these with some actual history texts, but they should give you some background and help for lit review.