For practical advice you need to consult a rabbi, but here is some general information.
Certain prayers/blessings, including the one said after lighting Shabbat candles, contain the phrase "who has commanded us". Gentiles haven't been commanded, so (a) saying it isn't accurate for you, and (b) you might be taking God's name in vain by saying it. (What exactly the Noachide prohibition on this is a separate question, but I mention this because at least some gentile religions also have this prohibition. If you are a member of such a religion and aren't yet sure you're leaving, you might care about that regardless of what Judaism has to say about it.)
But you aren't looking to practice exactly as an observant Jew does; you're exploring. There's nothing wrong with lighting candles and having a nice family dinner on Friday night, and if you want to use this time to focus more on your relationship with God, that's great! Instead of saying the standard candle blessing, you could say something like "thank you God for this special time", or even thank God for specific things that have gone well in the past week or that you're anticipating in the coming days. (Try not to make specific, mundane requests; Shabbat is about stepping out of ordinary time, and anyway, shouldn't God get to rest on Shabbat too?)
There is a special prayer said by some women after lighting candles that you could adapt. (You probably don't want to use it exactly as-is.) The text, from Aish HaTorah (h/t Isaac Moses):
May it be Your will, Lord my God and God of my fathers, to be gracious to me (and to my spouse, children, parents) and to all my family; grant us and all Israel good and long life; remember us for good and blessing; consider us for salvation and compassion; bless us with great blessings; make our household complete, crowning our home with the feeling of Your Divine Presence dwelling among us.
Make me worthy to raise learned children and grandchildren, who are wise and understanding, who love and fear God, people of truth, holy and attached to God, who will dazzle the world with Torah and goodness and service of God. Please hear our prayers, in the merit of our matriarchs Sarah, Rebecca, Rachel and Leah, and ensure that the glow of our lives will never be dimmed. Show us the glow of Your face and we will be saved. Amen.
To be clear: you aren't "doing Shabbat" by doing this, because Shabbat is a gift for the Jews, but you are setting aside some "God time" from the rest of your week, which is an important part of Shabbat. You probably don't want to call it "Shabbat" or "sabbath", though; it'll just confuse people.
If you do decide to explore conversion -- and not everybody who starts the process ends up converting; it really is exploration at that point and not commitment -- then the rabbi you work with will guide you in taking on practices. Most likely he will have you start saying the "who has commanded us" blessings before you are officially a Jew. But that's for your rabbi to decide; every case is different.