It really depends on what devices you are controlling. Many TV type devices use infrared light (IR), and you can make Arduino controls to mimic existing devices. Some controls use a different frequency than the common apps, and you might not be able to control those. Also, if the device uses bluetooth or wifi radio waves, it would much harder to reverse engineer the protocol. The usual place to go to for IR controls is Ken Shirriff's blog: A Multi-Protocol Infrared Remote Library for the Arduino. Be sure to get the newest versions, that are here: GitHub - Arduino-IRremote/Arduino-IRremote: Infrared remote library for Arduino: send and receive infrared signals with multiple protocols since the original version was made for an earlier version of the Arduino IDE, and things have changed.
In terms of hardware, pretty much any Arduino can control an IR light. If you want many buttons, you need to think about having an Arduino with more pins, or get shift registers to handle all of the imputs. So you might want to think about what you need in terms of keypad and buttons and battery control. I would say get a basic Arduino, an IR receiver, and and IR LED, and play with the IR learning code, and learn how to send various controls. It may be that for a hand held device, you ultimately may have to move away from the development boxes, but it would allow you to learn how to do the controls and get your feet wet.
I'm surprised that there aren't more kits to allow you to do what you want with minimal building. Unfortunately, most of the stuff is the opposite direction, where you have an IR controller, and you want to control the Arduino.