The biggest resource when it comes to freelancing, and indeed life, is time. Time is money is a cliche that we throw around a lot, but it's absolutely true, and in the context of freelancing, time is what freelancers tend to charge for in one way or another (be it by project or by the hour), and so it is really important to have equipment that can support your needs and not to hinder your performance or to slow you down.
The central piece for most freelancers is a laptop computer. The computer was invented to make things easier for humans, although sometimes, ironically, they make matters a lot worse. When you are charging somebody for your time, you can't charge them for the time that your laptop had frozen, shut you out of your browser, decided to spontaneously reset and then taken half an hour to turn back on again - your employers will expect you to have all the sufficient equipment within reason to complete your work with continuous flow. If your computer is showing some signs of age, it might be worth taking it in for a maintenance check up or to consider a replacement, because, god forbid, if you put this off too long it could completely break one day during a vital assignment with a tight deadline. Keep your software updated and keep your computer healthy for maximum efficiency resulting in maximum productivity output.
Much like having a working laptop, having a working internet connection is also absolutely vital for most freelance work. You can teach yourself to type without error at impossible speeds, but if your connection is slow, you will forever be waiting for your browser to load pages which, with today's technology, should be instant. This is particularly important for work that pays by the project as the more projects you can complete in an amount of time, the higher your income, and you will only be able to flit quickly between pages if your internet can keep up with you. You can check your connection quality and speeds using several applications or web based programmes. This can be difficult for those who wish to work remotely so that they can travel, because while many coffee shops and public establishments have free wifi, sometimes it is restricted by data use and slow, and can end up slowing down your work flow. If this is the case, it might be worth investing in a portable wireless router which operates from a sim card to ensure that you always have a trustworthy connection while you are in reception, although these can be expensive.
Software is just as equally as important as hardware. If your work is written, this is not so much a problem as most companies will usually request or accept documents written in Microsoft word, which is available on most operating platforms, but also most word processing applications will allow you to convert to a Microsoft document format, however for more specialised work which uses applications such as photo editing software or music editing software, there are often industry standard programmes such as Adobe Photoshop, which employers will expect you to be up to speed with, and while there are other applications which are perfectly capable of producing similar or even better results, you can't skim over the essentials that most employers will look for. While they don't always have to be your default editing programmes, it helps to be familiar with them as sometimes employers may specifically ask you.
Having the right equipment is an investment, as often it will set you back before you have even begun your work, but, over time, if it allows you to work quicker, more efficiently and more professionally, it should pay for itself and start to see a profit over making do with the basic tools that almost every modern person possesses. As well as saving you money, it can potentially save you a lot of patience, as technical problems are often very frustrating and stressful, particularly when deadlines are looming. Do yourself a favour and treat yourself to a nice laptop and some nice software, your wallet and your sanity will thank you later.