If the frame is much bigger the fabric will be very difficult to keep tight in the frame. Also if the fabric is heavy duty or very thin it can easily slip in ring frames. Wooden ring frames are preferable to the plastic ring frames as the fabric will slip more in a plastic frame than a wooden frame. My suggestion is to avoid ring frames and stick to the slightly more expensive square frame. You will enjoy working the embroidery much more and will get better results.
Stretcher bars are inexpensive embroidery frames in which the work can be pulled quite tight.
The bars are sold in pairs, with the end of the bars having teeth so that you can slot the bars together. Different length bars can be slotted together to match the size of your fabric. The fabric is pinned onto the bars using thumb tacks. These are good frames to work my kits in. You can pin the fabric along the top or on the sides of the frame.