Hey Tecike - the thing with BLW is to give Lo the 'same' food as the family. In the very early days I made food especially for LO and I to eat together, it didn't make a full meal for me though. But quickly moved on to 'real' food. So you really can and should just offer LO something from your regular diet. Within reason, no sugar, salt, honey etc. But one of the positive aspects of BLW is that if you start your LO on the food you usually eat then they get used to those flavours right from the off.
There is no need to start with carrots or any particular food, just whatever you want.
What sorts of food do you usually eat as a family?
Is it things like stews, meat, beans, mousaka, polenta? (sorry to be ignorant of your culture! I just googled it and this is what I read) My DS LOVES stews with beans, aubergine, courgettes (zuccini), tomatoes and red peppers. I usually chop the veg in quite big chunks so he can get hold of them.
My DS is not fond of potato unless it is roasted, in the early days I made some potato wedges (skins on, baked in the oven) sprinkled with some herbs or spices and he ate them but he went off them when he discovered there were other foods to eat!
Yes you can steam fruit, DS got lots of steamed apple wedges and pear wedges. They only take a minute or two though, do watch them or they turn to mush really quickly.
Soft fruits like melon, nectarine, papaya, mango, plum can be given without steaming.
You can offer fish and meat from 6 months too (UK guidelines other places are different).
And cooked beetroot - I LOVE it and don't get it nearly as often as I would like. That would be a lovely food to offer, but expect some stained clothes!