So basically the title says it all, but I'm currently on my third month of a phd in Estonia, in bioinformatics, though I am British.
The research is fine, I wouldn't say I was particularly motivated or enthusiastic about it, but I wouldn't describe it as hellish either.
My biggest issue is I don't have a lot of contact with other PhD students, as I am my supervisor's only phd student, and the others in the larger lab group are all lab-based researchers and have offices on another floor.
The other problem I have is as part of the PhD I have to take several courses, but the methods of signing up to the courses is confusing, and for an international student actually impossible to do without a big hassle sorting things out. I don't mind doing the courses, but it's just the stress involved in actually getting on the required modules is just really demotivating.
I should also add that I've had various anxiety/depression in the past, and certainly my anxiety has been triggered a lot since starting, I frequently feel inadequete, stupid and subsequently this lowers my motivation to do anything.

But I hestitate to quit because 1. I can sort out the issues with courses, and once I actually start them I will have the opportunity to meet more people, 3. The job situation back home and the fact I would probably also be lonely in my home town, as most of my friends have moved around the country/Europe, 4. Though I have recently realised what my ideal job would be, it's not something that you can rely on to gain an income, but I don't think I want to stick in academia/research either, 5. Worry of dissapointing my supervisor, and guilt over the grants etc

I was thinking of starting next term, and basically seeing how it goes, but is this best?

The first thing to say is that at the start of a PhD pretty much everyone feels inadequate and anxious - it's a big thing to start, and unknown territory, so that's perfectly normal.

The third month is very early to decide to quit, so if I were you I would stick it a while longer and see how it goes - but of course, you have to decide what you think is right for you.

It sounds like the contact with other PhD students would really help, and the courses would be a good way to make that contact. But if you're really unenthusiastic about the subject that would be more of a concern for me - you do have to immerse yourself in the research to get through. Of course, this early into a PhD you might not yet have found the bits that really will make it interesting for you, so again I'd give it a bit longer before deciding one way or the other.

The jobs market back home is another consideration - assuming you're actually being funded to do your studies, even if you do ultimately decide to quit, it's worth sticking at it until you have something else to go to, if you possibly can. But only you know how big an effect the experience is having on things like anxiety and depression - there's no point making yourself ill.

It sounds to me like you just need a bit of reassurance - and this forum is great for realising just how common all those insecurities actually are! I hope you come back to it all refreshed next term.

Do you want to get a PhD any more? If not, it might be right to quit but if it's still something that motivates you, I would give it more time. Like you say, doing the courses will help you meet people. Also is there an Erasmus society? Even if they're younger, it can be immensely helpful to share the stranger aspects of your new country with other foreigners. Estonian language classes (yes I know it's an impossible language) might also help you meet people in a similar position.
I just wanted to add that you're also living in a new country and in about the time period when the honeymoon period when everything is new and exciting is over, and all you can see is the difficulties in living in a different country and the things you don't like. Google culture shock - you might find yourself recognising a few of your feelings in the description. From experience, it does get better but you've got to make a conscious effort to keep busy to get through the tough time. Think about how you can do the things you like to do there, plan weekend sightseeing trips etc - anything that gets you out of the house and distracts you will help a bit.