*To me*, 拎 is
1) an old-fashioned term but somehow showing a profound knowledge of Mandarin Chinese language,
e.g. 她提著包包逛街去 - okay, I got you.
e.g. 她拎著包包逛街去 - wow, your Mandarin is very very very good!
2) much limited in usage,
e.g. I would say 提款 'withdraw money' but never 拎款.
e.g. I would say 提筆寫字 (simplified: 提笔写字) 'take the pen and write' but never 拎筆寫字.
e.g. I would say 提及 'mention' but never 拎及.
3) carrying light-weighted stuff and for ladies or children particularly.
e.g. 小女孩拎著鞋子在沙灘 (simplified: 滩) 上走 - okay.
e.g. 媽媽 (simplified: 妈妈) 拎著鞋子在沙灘上走 - okay.
e.g. 爸爸拎著鞋子在沙灘上走 - hmm, if I were you I would say 拿 rather than 拎.
Hope I helped :-)