Common causes of equipment damage or failure are rapid power cycling and surges. Protection does not require a large capacity UPS but does require good quality power filtering. A large capacity UPS will do more to prevent loss of recordings and will often provide better power filtering.
Shaw 630 PVRs draw about 20w, probably less for the 830. An external hard drive will be about 10w max. That's 70w. Multiply by 2 for worst case VA and by 2 again for 50% load. That's a conservative requirement of 280VA. A 350VA would provide at least 10 minutes of run time. (APC BK350) That UPS does not have the required 4 battery powered outlets and it is probably discontinued. Beware of old stock since UPS batteries do not keep well over 6 months without being recharged.
A 450VA UPS (APC BE450G-CN) would provide at least 20 minutes of run time under the same conditions. It has the required 4 backup outlets. The 650VA BE650G1-CN offers about 40 minutes of run time. The 750VA BE750G-CN offers 50 minutes of run time so it's battery capacity is not significantly higher than the 650VA model. It looks like APC is in the middle of revamping their product lines so availability on those models may be limited or only newer models with slightly different specs may be available.
Extra run time is provided by higher capacity batteries in higher powered UPS, not the extra VA. The higher capacity models often also have extra features such as USB charging ports, better energy efficiency, better UPS monitoring or control, LCD displays for status and more outlets.
Another consideration when buying a UPS is overall efficiency. Higher powered models tend to draw more standby power. Newer models tend to draw less standby power, lowering electricity bills and producing less heat.