Hi Touzo and welcome.
Since you are already vegetarian, your food transition will be a question of substituting for/eliminating cow dairy and chicken eggs. The main thing is to make sure you get enough to eat. Vegan food is less calorie dense, so many new vegans become tired and weak, blaming it on iron, protein, B12...when it is simply a lack of enough calories.
There are some great vegan food blogs out there, great cookbooks etc. Since you already apparently know how to cook, adapting your recipes won't be difficult. Plant milks for cow milk, etc. Cheese is an issue for many transitioning. The nondairy cheeses are different than the cow or goat cheeses. Spices and herbs are your friends, and whole grains, legumes, vegetables, and fruits (in season) are cheap, easy, and nutritious. Root vegetables in particular are filli g and fantastic.
Best of luck, and make sure you check out the What are you eating vegan today type threads here for great ideas. [emoji173]