For less than 2000 records, you might even use MS Excel. Access is WOW!, and Oracle is overkill.
XE will be installed without problems. You'll need to transfer data from Access to Oracle (do you know SQL*Loader, for example?). Having data in a table is not enough because you'll need to create front-end for your user(s). XE offers Application Builder which will help you create simple forms/reports, but - is that enough? If not, you'll need to learn something more about (PL/)SQL programming in Oracle.
If you, finally, choose to use Oracle XE, I believe you won't regret. It contains almost all functionalities as a "real, grown-up" Oracle database.