This is basically a question of Virtual Reality vs Augmented Reality. As a Decker, you will be connected to the Matrix pretty much all the time. Whenever you aren't in VR for the dice pool bonuses (which renders your meatspace body unconscious), you should be in AR.
You'll still be able to perceive and interact with the Matrix icons of other devices and personas (which show up as AROs or augmented reality objects), including the icon belonging to the Agent (which is autonomous) running on your cheap cyberdeck. As long as the Agent is running (and it should be running all the time once you load it onto the deck), you can send it commands which it will execute to the best of its ability. It even has its own slot in the initiative order if you decide to send it commands in the middle of combat.
Note that if you want to be able to mentally interact with the Matrix via AR or send commands (such as activating or deactivating a program like an Agent) to your wireless devices (such as cyberdecks, comlinks, guns, etcetera) outside of VR then you need a DNI (direct neural interface). When it comes to obtaining a DNI as a Decker, you have two options: Trodes or a Datajack. Even if you choose to forego a DNI and you want to physically interact with AROs, to get the "full experience" (sight, sound, and touch) then you need eyewear with Image Link, earwear with Sound Link, and either AR Gloves or a full-body suit with the Tactile Feedback modification.
Note that the relevant sections of the SR5 Core Rulebook for more information on VR vs AR are a bit too lengthy to reproduce verbatim in this answer so I will simply refer you to pages 221-223.
SR5 Core Rulebook, Agents, Page 246.
Agents are autonomous programs that are rated from 1 to 6. Each agent occupies one program slot on your deck. Agents use the Matrix attributes of the device they run on, and their rating (up to 6) for attributes. Agents also have the Computer, Hacking, and Cybercombat skills at a rating equal to their own. An agent runs as a program and can use programs running on the same device as them.
You can have your agent perform Matrix actions for you. When an agent is running, it has its own persona (and icon). An agent is about as smart as a pilot program of the same rating (Pilot Programs, p. 269).