It obviously depends on your goals - building size? endurance training? improving agility?
If you want to add size, then you need to start off with a good weights set. Make sure you invest in a good bench that offers a variety of angles, a barbell, dumbbell bars and weight plates. To start with, you won't need anymore than 50 or so kilograms - the average starter kit weight (you can always add more when you get stronger). A multipurpose chin up bar is an awesome addition too. They are cheap and you can perform a variety of exercises on them - chin ups, pull ups, press ups, dips, and crunches (the ones that hook onto a door frame). An ab wheel is another cheap piece of kit that is very effective. That is a good position to start from - you can always add more to it over time, but if you're a beginner, the that will get you started). There's a lot of awesome exercises you can perform with just a barbell and dumbbells.
If you're looking to go into endurance training, then you need to choose what kind - running? cycling? rowing? One of those pieces of equipment won't be cheap, but once you buy them, there's no monthly cost (unlike a gym membership). You can however pick up a bargain by going down the refurbished equipment route.
Improving agility at home is cheap, as long as you have room to train. Mini hurdles, a performance ladder, ankle weights, skipping rope, jump box, just to name a few, are inexpensive but effective.
Training at home is doable and can be productive, if you select the right equipment and can motivate yourself to train hard.
Lee Gregory Fitness