A furnished rental already has more than most people expect. Packing for one is different than packing for a hotel or an empty apartment. Here's what's usually covered, and what's worth bringing anyway.

Start with the kitchen. A furnished unit almost always includes basic cookware, plates, glasses, and utensils. You won't need to bring pots or a full set of dishes. What's worth packing is anything specific to how you actually cook. If you use a particular spice blend daily, or you need a coffee setup beyond a basic drip machine, bring that. The kitchen will work fine, but it won't match your kitchen exactly.
Bedding and towels are usually provided too, including sheets, pillows, and at least one set of towels per guest. If you're picky about pillow firmness, or you always travel with your own pillow, pack it. Otherwise, this is one less thing to think about.

Toiletries are where people overpack the most. Furnished units rarely stock shampoo or toothpaste beyond maybe a starter bottle. Bring your actual toiletries, but skip packing a full month's supply if there's easy access to a grocery store nearby. Buying a bit more once you're settled almost always beats hauling extra weight in a bag.
Laundry supplies are a common miss. Most furnished apartments have an in-unit washer and dryer, but detergent isn't always included. Bring a small travel-size detergent for your first load, or plan to grab some the day you arrive.
Work setup matters if you're staying for a job or a rotation. Wi-Fi is included everywhere, but check the listing for real desk space before you arrive if you need a proper workspace. A laptop stand or an external mouse can make a real difference over a multi-week stay, even though neither takes up much room in a bag.

Weather is worth checking specifically for Houston. Summers run hot and humid, and most buildings are air-conditioned aggressively. A light layer for indoors isn't a bad idea even in July. Winters are mild but can turn cold for a few days at a time. One warmer layer covers most cold snaps without needing a full winter wardrobe.
Documents matter more than people expect. Bring a physical or digital copy of your ID for verification. Keep your confirmation details handy for check-in day too, since the door code and directions usually arrive by text the morning you arrive.
One last thing worth packing: a phone charger that reaches the bed. It sounds small, but it's the item people forget most often, and it's rarely one a furnished unit provides.
Pack for the stay you're actually taking, not for a hotel where nothing is provided. Most of what people over-pack for a furnished rental turns out to already be there.