Most of the time people pay attention to cycle reservations, not always I will grant you that, and some people take up the whole of a space allocated for two cycles with an oversized e-bike which didn't fit the space. This was on an IET some time ago, let's not go into how unhelpful that was, thankfully though there was another option on my quiet train and I boarded at the start of the journey.
Voyagers and cycles, those who have commented so far are incorrect. There is more than one space on Voyagers for cycles. Officially, there's two sections in each Voyager, one is meant to fit two cycles and the other, according to the information sticker, is supposed to be kept as a spare. This is all fine and good if your cycle is quite small or whatever, but I found in practice that it was nigh-on impossible to fit my hybrid cycle in the space designed (supposedly) for two cycles. I took the 'spare' space when I did Birmingham to Derby back in January. Even then, it only just fitted into that space!
One thing I will say is that the hooks were a lot more lenient than those found on IETs. Which is certainly good news! So while I would suggest you might have difficulty in getting your cycle in/out of the Voyager, the lifting the front/rear wheel up enough to get it onto the hook is not quite as challenging as on a GWR IET.
Regarding the reservation, you should receive a cycle reservation ticket when you pick up your travel tickets. Well, two reservations. One should be attached to the cycle (I usually stick mine alongside the bottle on one of the bottle cages) and one to be kept with you. Almost no-one seems to display their reservation on their cycle, and occasionally I will confess to not doing so myself. On said reservation, it should have a carriage letter on it, which is where your reservation should be. I haven't got one here to confirm this right now, but it is how it normally is on my travels.
Would I recommend standing next to your cycle on your journey? No, that's not really going to be enjoyable. On a short leap, maybe so, but Oxford-Stafford is a fair trek and you'll want to sit down on that journey. I'd recommend finding an unreserved seat near your cycle, absolutely, if only for peace of mind that you'll get from being able to keep an eye on it at station stops.
Panniers etc, I would remove before boarding, as they will make loading your cycle much harder and possibly infringe on someone else's space.
At the time you're travelling, I don't personally think it would be an issue, so I'd be confident of travelling safely with your cycle. Whatever the purpose of your journey is, I hope it's a good one. Finally for now, happy cycling!
If you have a digital reservation, I would simply screenshot the message and the confirmation. Save paper where possible!