Corinne's Mommy,
first off WELCOME! You and your lo will love BLW. So good htat she is putting things in her mouth already! Don't push it, just let her explore. Some of the best things to start with are exactly what you have and basically anything soft. avocado, sweet potato, pear etc. Try and make it a size that she can hold - so a large chip! - and soft enough for it to dissolve in her mouth but hard enough to hold. hard iwth some things like avo. if it's slippery, which is a challenge at first, roll in wheatgerm or cheerio dust etc. anything that will take the slippery away.
And yes, personally I would at her age to intro foods every few days to gauge reactions. I'm a little more lax now, but still try and not intro new foods too close together. If you have allergies, these are the ones I would leave until older and definately give by itself and give it a good few days to see for reaction.
hth