Catch-up services, such as iPlayer and All 4, AREN'T transmitted from terrestrial aerials. The ONLY way that you can access them is via the internet. So you'll definitely NEED a 'smart' TV (i.e. one that can connect to the internet). However, although you'll be accessing catch-up services over the internet, you'll still be receiving your regular channels via your aerial (either directly or via your Humax box).
Smart TVs don't have 'holes' to make their connection online; they simply pick up a wifi signal from your broadband router. Any modern telly is likely to have two (or more) HDMI input sockets, enabling you to connect both your Humax box and your DVD player to your TV set without any problems.
If you give us an idea of the size of the set you require, we'll be able to point you towards some suitable recommendations.