If you can show that you relocated for work purposes you can make a claim for your relocation expenses. In most cases it is sufficient to show that you took up work in Germany within a reasonable period after relocating. You can claim the cost of transport for yourself and all members of your family and there is no absolute limit on the cost of such transport. So you do not need to look for the cheapest flight ticket. You can also claim the cost for transporting personal belongings – your entire household actually. And you can claim the cost of finding accommodation in Germany. This would include if you had to come here before your actual move to check out the area and go looking for a house, etc.
What happens if you leave all your furniture behind and buy all new stuff when you move to Germany? The answer seems a bit silly at first glance: If you had shipped all your old furniture, you could have claimed the cost of transport. If you buy all new, you cannot claim anything. Why? You had an old chair before and you could have sold the old chair and used the funds to buy a new one. And even if the new one is more expensive, then you have upgraded your household to a better chair (according to tax office logic, you have not lost anything – so there is no need for tax relief). The cost of transport on the other hand is a definitive expense. After your move and after incurring the cost of transport you still own the same old chair. This justifies tax relief.
Even if you had none of the above or your employer paid for all, you will still qualify for some standard relocation deduction without showing any receipts. The amounts increase with every extra member of your family.