Before you drywall over anything
If you're standing in your basement measuring for a stud wall or picking out flooring samples, stop for a week and just watch the space instead. West Chester basements go through a real cycle every year, from soggy springs when the water table sits high to dry, cold winters when the ground contracts around the foundation. A basement that looks fine in October can tell a different story in April. Before you spend money finishing it, you want to know which version of the basement you're actually building on top of.
What the local ground and houses are doing to that basement
Chester County has a lot of clay and shale-heavy soil, and a lot of homes built between the 1920s and the 1980s with stone or block foundations that were never meant to be fully waterproofed the way a modern poured foundation is. Older stone foundations in particular were built assuming some dampness would pass through, which is why so many of them have a slightly musty smell no matter what you do. Newer block foundations from the mid-century building boom have their own issue: the mortar joints and the cores of the block itself are common points where water finds a way in after thirty or forty years.
On top of that, this region gets a real freeze-thaw cycle each winter. Water gets into small cracks in the foundation, freezes, expands, and widens the crack a little more. It's slow, but it's consistent, and it's why a basement that was watertight when the house was built can develop a seep line along one wall decades later.
More on this from basement remodeling around West Chester.
What to check yourself, right now
Walk the perimeter of the basement after a heavy rain, not on a dry day. Look for damp patches on the walls, especially where they meet the floor, and look at the floor itself for white, chalky mineral deposits, which usually mean water has been wicking through and evaporating there for a while. Check the corners near window wells, since older window wells in this area often fill with leaves and silt and stop draining the way they were designed to.
Outside, look at your gutters and downspouts. A huge number of wet basement problems in this region trace back to a downspout dumping water two feet from the foundation instead of six or eight feet away. Grade matters too. If the ground slopes toward the house instead of away from it, which happens often on the older, hillier lots around West Chester, water is going to find the foundation no matter what you do inside.
Check for a sump pump. If there is one, run it manually and watch where the discharge line actually goes. A lot of older systems dump water right next to the foundation, which just recycles the same water back into the ground you're trying to keep dry.
Where this stops being a weekend project
If you find active water, meaning wet walls or standing water rather than just old staining, that needs to be solved before any framing goes in, and it usually needs someone who does foundation and drainage work for a living. The same goes for any crack wider than a pencil, any bowing in a foundation wall, or any spot where the mortar between stones or blocks is crumbling and coming out when you touch it. Those are structural questions, not cosmetic ones, and covering them with a finished wall just hides the problem until it's worse and more expensive.
Radon is also worth a real test, not a guess. Chester County sits in an area with elevated radon readings, and a finished basement with less air exchange can trap it at higher concentrations than an open, unfinished one. A test kit is cheap and simple. If the numbers come back high, that's a mitigation system, which is a specialized install, not a DIY fix.
What a good finish job assumes is already true
Any basement remodeling done right in this area starts with the assumption that the space will get damp air in summer, whether or not it currently shows water. That means vapor barriers, the right kind of insulation for a below-grade wall, and materials on the lower few inches of any wall that can handle occasional moisture without falling apart. It also usually means a dehumidifier running most of the year, because central air conditioning alone doesn't pull enough moisture out of a below-grade space.
None of this is about scaring you off finishing the basement. Plenty of basements in West Chester get finished successfully every year. It's about spending the first weeks looking at the water, the grade, and the foundation instead of the paint colors, so the finished room you build doesn't end up hiding a problem you'll be paying to fix twice.