Bedside table lamps are hugely diverse in styles and function. Some table lamps provide discreet reading light whilst others offer blooms of light to fill your bedside with cheerful, ambient light. There are table lamps with shades, with directional spot lights, articulated arms, small bases, thumbswitches, touch dim, and a massive range of finishes and materials. 

Things to consider is the size of the base in relation to your night table (don't worry if you haven't got room on your night table for a table lamp - consider a pendant or a wall mounted plug-in light that you can mount above the table to get the same lovely lighting). Another thing to think about is the height of the light - low level lighting is really nice way to create a peaceful vibe and taller lights will give more light. 

And if you have a bouncy pet or little one running around, perhaps avoid table lamps with tippy glass shades (though they do give a lovely glow!). 

Definitely make room in your budget and bedroom scheme for these little (or big!) hero's, you won't regret it (and you'll use it every day - or night rather).