No different than golf gear - the answer is always "Of course you do!"
For a practice amp, take a look at the Positive Grid Spark. It's a fun little amp - plenty loud enough for home and the digital modeling allows you to get a ton of different tones, everything from acoustic to full-on metal. It connects via Bluetooth to your phone or tablet, which is where you play with all the amps and effects modeling. It also gives you a metronome, access to a ton of jam tracks that play through the amp via Bluetooth, and you can also connect to Spotify, Apple Music and YouTube to play along to songs. And when you're not using it for guitar, it's a pretty cool Bluetooth speaker to play music through. Has a headphone jack for silent practice, and can also connect to your computer as a USB interface for recording. Looks like they're on sale for $254 right now at their website, they're really a lot of bang for the buck. I bought mine about a month ago and have been having a blast with it. You can also buy an external rechargeable battery pack (the kind that can power a laptop), and then you can use the amp anywhere without needing a wall plug.
As far as cheap guitars - I don't have any first-hand experience with them, but I've seen a lot of buzz about Harley Benton guitars lately. They're priced very reasonably and the reviews I've seen say the quality is really good for the price. Only downside I can see is that they're sold through thomann.de in Germany, so I don't know what the shipping time to the U.S. is like.
That is a great tip on the positive grid Spark. I will look into it, it sounds really versatile!